Daily Papers

The variability of wind power supply can present substantial challenges to incorporating wind power into a grid system. Thus, Wind Power Forecasting (WPF) has been widely recognized as one of the most critical issues in wind power integration and operation. There has been an explosion of studies on wind power forecasting problems in the past decades. Nevertheless, how to well handle the WPF problem is still challenging, since high prediction accuracy is always demanded to ensure grid stability and security of supply. We present a unique Spatial Dynamic Wind Power Forecasting dataset: SDWPF, which includes the spatial distribution of wind turbines, as well as the dynamic context factors. Whereas, most of the existing datasets have only a small number of wind turbines without knowing the locations and context information of wind turbines at a fine-grained time scale. By contrast, SDWPF provides the wind power data of 134 wind turbines from a wind farm over half a year with their relative positions and internal statuses. We use this dataset to launch the Baidu KDD Cup 2022 to examine the limit of current WPF solutions. The dataset is released at https://aistudio.baidu.com/aistudio/competition/detail/152/0/datasets.

Spatiotemporal forecasting techniques are significant for various domains such as transportation, energy, and weather. Accurate prediction of spatiotemporal series remains challenging due to the complex spatiotemporal heterogeneity. In particular, current end-to-end models are limited by input length and thus often fall into spatiotemporal mirage, i.e., similar input time series followed by dissimilar future values and vice versa. To address these problems, we propose a novel self-supervised pre-training framework Spatial-Temporal-Decoupled Masked Pre-training (STD-MAE) that employs two decoupled masked autoencoders to reconstruct spatiotemporal series along the spatial and temporal dimensions. Rich-context representations learned through such reconstruction could be seamlessly integrated by downstream predictors with arbitrary architectures to augment their performances. A series of quantitative and qualitative evaluations on six widely used benchmarks (PEMS03, PEMS04, PEMS07, PEMS08, METR-LA, and PEMS-BAY) are conducted to validate the state-of-the-art performance of STD-MAE. Codes are available at https://github.com/Jimmy-7664/STD-MAE.

Accurate weather forecasts are important for disaster prevention, agricultural planning, etc. Traditional numerical weather prediction (NWP) methods offer physically interpretable high-accuracy predictions but are computationally expensive and fail to fully leverage rapidly growing historical data. In recent years, deep learning models have made significant progress in weather forecasting, but challenges remain, such as balancing global and regional high-resolution forecasts, excessive smoothing in extreme event predictions, and insufficient dynamic system modeling. To address these issues, this paper proposes a global-regional nested weather forecasting framework (OneForecast) based on graph neural networks. By combining a dynamic system perspective with multi-grid theory, we construct a multi-scale graph structure and densify the target region to capture local high-frequency features. We introduce an adaptive messaging mechanism, using dynamic gating units to deeply integrate node and edge features for more accurate extreme event forecasting. For high-resolution regional forecasts, we propose a neural nested grid method to mitigate boundary information loss. Experimental results show that OneForecast performs excellently across global to regional scales and short-term to long-term forecasts, especially in extreme event predictions. Codes link https://github.com/YuanGao-YG/OneForecast.

A data-driven model (DDM) suitable for regional weather forecasting applications is presented. The model extends the Artificial Intelligence Forecasting System by introducing a stretched-grid architecture that dedicates higher resolution over a regional area of interest and maintains a lower resolution elsewhere on the globe. The model is based on graph neural networks, which naturally affords arbitrary multi-resolution grid configurations. The model is applied to short-range weather prediction for the Nordics, producing forecasts at 2.5 km spatial and 6 h temporal resolution. The model is pre-trained on 43 years of global ERA5 data at 31 km resolution and is further refined using 3.3 years of 2.5 km resolution operational analyses from the MetCoOp Ensemble Prediction System (MEPS). The performance of the model is evaluated using surface observations from measurement stations across Norway and is compared to short-range weather forecasts from MEPS. The DDM outperforms both the control run and the ensemble mean of MEPS for 2 m temperature. The model also produces competitive precipitation and wind speed forecasts, but is shown to underestimate extreme events.

Predictive maintenance (PdM) is increasingly pursued to reduce wind farm operation and maintenance costs by accurately predicting the remaining useful life (RUL) and strategically scheduling maintenance. However, the remoteness of wind farms often renders current methodologies ineffective, as they fail to provide a sufficiently reliable advance time window for maintenance planning, limiting PdM's practicality. This study introduces a novel deep learning (DL) methodology for future RUL forecasting. By employing a multi-parametric attention-based DL approach that bypasses feature engineering, thereby minimizing the risk of human error, two models: ForeNet-2d and ForeNet-3d are proposed. These models successfully forecast the RUL for seven multifaceted wind turbine (WT) failures with a 2-week forecast window. The most precise forecast deviated by only 10 minutes from the actual RUL, while the least accurate prediction deviated by 1.8 days, with most predictions being off by only a few hours. This methodology offers a substantial time frame to access remote WTs and perform necessary maintenance, thereby enabling the practical implementation of PdM.

Predictive Coding (PC) is a theoretical framework in cognitive science suggesting that the human brain processes cognition through spatiotemporal prediction of the visual world. Existing studies have developed spatiotemporal prediction neural networks based on the PC theory, emulating its two core mechanisms: Correcting predictions from residuals and hierarchical learning. However, these models do not show the enhancement of prediction skills on real-world forecasting tasks and ignore the Precision Weighting mechanism of PC theory. The precision weighting mechanism posits that the brain allocates more attention to signals with lower precision, contributing to the cognitive ability of human brains. This work introduces the Cognitive Diffusion Probabilistic Models (CogDPM), which demonstrate the connection between diffusion probabilistic models and PC theory. CogDPM features a precision estimation method based on the hierarchical sampling capabilities of diffusion models and weight the guidance with precision weights estimated by the inherent property of diffusion models. We experimentally show that the precision weights effectively estimate the data predictability. We apply CogDPM to real-world prediction tasks using the United Kindom precipitation and ERA surface wind datasets. Our results demonstrate that CogDPM outperforms both existing domain-specific operational models and general deep prediction models by providing more proficient forecasting.

Accuracy and timeliness are indeed often conflicting goals in prediction tasks. Premature predictions may yield a higher rate of false alarms, whereas delaying predictions to gather more information can render them too late to be useful. In applications such as wildfires, crimes, and traffic jams, timely forecasting are vital for safeguarding human life and property. Consequently, finding a balance between accuracy and timeliness is crucial. In this paper, we propose an early spatio-temporal forecasting model based on Multi-Objective reinforcement learning that can either implement an optimal policy given a preference or infer the preference based on a small number of samples. The model addresses two primary challenges: 1) enhancing the accuracy of early forecasting and 2) providing the optimal policy for determining the most suitable prediction time for each area. Our method demonstrates superior performance on three large-scale real-world datasets, surpassing existing methods in early spatio-temporal forecasting tasks.

Accurate forecasts for day-ahead photovoltaic (PV) power generation are crucial to support a high PV penetration rate in the local electricity grid and to assure stability in the grid. We use state-of-the-art tree-based machine learning methods to produce such forecasts and, unlike previous studies, we hereby account for (i) the effects various meteorological as well as astronomical features have on PV power production, and this (ii) at coarse as well as granular spatial locations. To this end, we use data from Belgium and forecast day-ahead PV power production at an hourly resolution. The insights from our study can assist utilities, decision-makers, and other stakeholders in optimizing grid operations, economic dispatch, and in facilitating the integration of distributed PV power into the electricity grid.

Knowledge about the hidden factors that determine particular system dynamics is crucial for both explaining them and pursuing goal-directed interventions. Inferring these factors from time series data without supervision remains an open challenge. Here, we focus on spatiotemporal processes, including wave propagation and weather dynamics, for which we assume that universal causes (e.g. physics) apply throughout space and time. A recently introduced DIstributed SpatioTemporal graph Artificial Neural network Architecture (DISTANA) is used and enhanced to learn such processes, requiring fewer parameters and achieving significantly more accurate predictions compared to temporal convolutional neural networks and other related approaches. We show that DISTANA, when combined with a retrospective latent state inference principle called active tuning, can reliably derive location-respective hidden causal factors. In a current weather prediction benchmark, DISTANA infers our planet's land-sea mask solely by observing temperature dynamics and, meanwhile, uses the self inferred information to improve its own future temperature predictions.

Weather forecasting is one of the cornerstones of meteorological work. In this paper, we present a new benchmark dataset named Weather2K, which aims to make up for the deficiencies of existing weather forecasting datasets in terms of real-time, reliability, and diversity, as well as the key bottleneck of data quality. To be specific, our Weather2K is featured from the following aspects: 1) Reliable and real-time data. The data is hourly collected from 2,130 ground weather stations covering an area of 6 million square kilometers. 2) Multivariate meteorological variables. 20 meteorological factors and 3 constants for position information are provided with a length of 40,896 time steps. 3) Applicable to diverse tasks. We conduct a set of baseline tests on time series forecasting and spatio-temporal forecasting. To the best of our knowledge, our Weather2K is the first attempt to tackle weather forecasting task by taking full advantage of the strengths of observation data from ground weather stations. Based on Weather2K, we further propose Meteorological Factors based Multi-Graph Convolution Network (MFMGCN), which can effectively construct the intrinsic correlation among geographic locations based on meteorological factors. Sufficient experiments show that MFMGCN improves both the forecasting performance and temporal robustness. We hope our Weather2K can significantly motivate researchers to develop efficient and accurate algorithms to advance the task of weather forecasting. The dataset can be available at https://github.com/bycnfz/weather2k/.

Spatio-Temporal Graph (STG) forecasting is a fundamental task in many real-world applications. Spatio-Temporal Graph Neural Networks have emerged as the most popular method for STG forecasting, but they often struggle with temporal out-of-distribution (OoD) issues and dynamic spatial causation. In this paper, we propose a novel framework called CaST to tackle these two challenges via causal treatments. Concretely, leveraging a causal lens, we first build a structural causal model to decipher the data generation process of STGs. To handle the temporal OoD issue, we employ the back-door adjustment by a novel disentanglement block to separate invariant parts and temporal environments from input data. Moreover, we utilize the front-door adjustment and adopt the Hodge-Laplacian operator for edge-level convolution to model the ripple effect of causation. Experiments results on three real-world datasets demonstrate the effectiveness and practicality of CaST, which consistently outperforms existing methods with good interpretability.

The Copernicus Regional Reanalysis for Europe, CERRA, is a high-resolution regional reanalysis dataset for the European domain. In recent years it has shown significant utility across various climate-related tasks, ranging from forecasting and climate change research to renewable energy prediction, resource management, air quality risk assessment, and the forecasting of rare events, among others. Unfortunately, the availability of CERRA is lagging two years behind the current date, due to constraints in acquiring the requisite external data and the intensive computational demands inherent in its generation. As a solution, this paper introduces a novel method using diffusion models to approximate CERRA downscaling in a data-driven manner, without additional informations. By leveraging the lower resolution ERA5 dataset, which provides boundary conditions for CERRA, we approach this as a super-resolution task. Focusing on wind speed around Italy, our model, trained on existing CERRA data, shows promising results, closely mirroring original CERRA data. Validation with in-situ observations further confirms the model's accuracy in approximating ground measurements.

As Chile's electric power sector advances toward a future powered by renewable energy, accurate forecasting of renewable generation is essential for managing grid operations. The integration of renewable energy sources is particularly challenging due to the operational difficulties of managing their power generation, which is highly variable compared to fossil fuel sources, delaying the availability of clean energy. To mitigate this, we quantify the impact of increasing intermittent generation from wind and solar on thermal power plants in Chile and introduce a hybrid wind speed forecasting methodology which combines two custom ML models for Chile. The first model is based on TiDE, an MLP-based ML model for short-term forecasts, and the second is based on a graph neural network, GraphCast, for medium-term forecasts up to 10 days. Our hybrid approach outperforms the most accurate operational deterministic systems by 4-21% for short-term forecasts and 5-23% for medium-term forecasts and can directly lower the impact of wind generation on thermal ramping, curtailment, and system-level emissions in Chile.

Analyzing both temporal and spatial patterns for an accurate forecasting model for financial time series forecasting is a challenge due to the complex nature of temporal-spatial dynamics: time series from different locations often have distinct patterns; and for the same time series, patterns may vary as time goes by. Inspired by the successful applications of deep learning, we propose a new model to resolve the issues of forecasting household leverage in China. Our solution consists of multiple RNN-based layers and an attention layer: each RNN-based layer automatically learns the temporal pattern of a specific series with multivariate exogenous series, and then the attention layer learns the spatial correlative weight and obtains the global representations simultaneously. The results show that the new approach can capture the temporal-spatial dynamics of household leverage well and get more accurate and solid predictive results. More, the simulation also studies show that clustering and choosing correlative series are necessary to obtain accurate forecasting results.

Accurate and reliable energy time series prediction is of great significance for power generation planning and allocation. At present, deep learning time series prediction has become the mainstream method. However, the multi-scale time dynamics and the irregularity of real data lead to the limitations of the existing methods. Therefore, we propose EnergyPatchTST, which is an extension of the Patch Time Series Transformer specially designed for energy forecasting. The main innovations of our method are as follows: (1) multi-scale feature extraction mechanism to capture patterns with different time resolutions; (2) probability prediction framework to estimate uncertainty through Monte Carlo elimination; (3) integration path of future known variables (such as temperature and wind conditions); And (4) Pre-training and Fine-tuning examples to enhance the performance of limited energy data sets. A series of experiments on common energy data sets show that EnergyPatchTST is superior to other commonly used methods, the prediction error is reduced by 7-12%, and reliable uncertainty estimation is provided, which provides an important reference for time series prediction in the energy field.

While diffusion models can successfully generate data and make predictions, they are predominantly designed for static images. We propose an approach for efficiently training diffusion models for probabilistic spatiotemporal forecasting, where generating stable and accurate rollout forecasts remains challenging, Our method, DYffusion, leverages the temporal dynamics in the data, directly coupling it with the diffusion steps in the model. We train a stochastic, time-conditioned interpolator and a forecaster network that mimic the forward and reverse processes of standard diffusion models, respectively. DYffusion naturally facilitates multi-step and long-range forecasting, allowing for highly flexible, continuous-time sampling trajectories and the ability to trade-off performance with accelerated sampling at inference time. In addition, the dynamics-informed diffusion process in DYffusion imposes a strong inductive bias and significantly improves computational efficiency compared to traditional Gaussian noise-based diffusion models. Our approach performs competitively on probabilistic forecasting of complex dynamics in sea surface temperatures, Navier-Stokes flows, and spring mesh systems.

Time series forecasting is central to decision-making in domains as diverse as energy, finance, climate, and public health. In practice, forecasters face thousands of short, noisy series that vary in frequency, quality, and horizon, where the dominant cost lies not in model fitting, but in the labor-intensive preprocessing, validation, and ensembling required to obtain reliable predictions. Prevailing statistical and deep learning models are tailored to specific datasets or domains and generalize poorly. A general, domain-agnostic framework that minimizes human intervention is urgently in demand. In this paper, we introduce TimeSeriesScientist (TSci), the first LLM-driven agentic framework for general time series forecasting. The framework comprises four specialized agents: Curator performs LLM-guided diagnostics augmented by external tools that reason over data statistics to choose targeted preprocessing; Planner narrows the hypothesis space of model choice by leveraging multi-modal diagnostics and self-planning over the input; Forecaster performs model fitting and validation and, based on the results, adaptively selects the best model configuration as well as ensemble strategy to make final predictions; and Reporter synthesizes the whole process into a comprehensive, transparent report. With transparent natural-language rationales and comprehensive reports, TSci transforms the forecasting workflow into a white-box system that is both interpretable and extensible across tasks. Empirical results on eight established benchmarks demonstrate that TSci consistently outperforms both statistical and LLM-based baselines, reducing forecast error by an average of 10.4% and 38.2%, respectively. Moreover, TSci produces a clear and rigorous report that makes the forecasting workflow more transparent and interpretable.

Modern techniques for physical simulations rely on numerical schemes and mesh-refinement methods to address trade-offs between precision and complexity, but these handcrafted solutions are tedious and require high computational power. Data-driven methods based on large-scale machine learning promise high adaptivity by integrating long-range dependencies more directly and efficiently. In this work, we focus on fluid dynamics and address the shortcomings of a large part of the literature, which are based on fixed support for computations and predictions in the form of regular or irregular grids. We propose a novel setup to perform predictions in a continuous spatial and temporal domain while being trained on sparse observations. We formulate the task as a double observation problem and propose a solution with two interlinked dynamical systems defined on, respectively, the sparse positions and the continuous domain, which allows to forecast and interpolate a solution from the initial condition. Our practical implementation involves recurrent GNNs and a spatio-temporal attention observer capable of interpolating the solution at arbitrary locations. Our model not only generalizes to new initial conditions (as standard auto-regressive models do) but also performs evaluation at arbitrary space and time locations. We evaluate on three standard datasets in fluid dynamics and compare to strong baselines, which are outperformed both in classical settings and in the extended new task requiring continuous predictions.

Many data have an underlying dependence on spatial location; it may be weather on the Earth, a simulation on a mesh, or a registered image. Yet this feature is rarely taken advantage of, and violates common assumptions made by many neural network layers, such as translation equivariance. Further, many works that do incorporate locality fail to capture fine-grained structure. To address this, we introduce the Spatial Mixture-of-Experts (SMoE) layer, a sparsely-gated layer that learns spatial structure in the input domain and routes experts at a fine-grained level to utilize it. We also develop new techniques to train SMoEs, including a self-supervised routing loss and damping expert errors. Finally, we show strong results for SMoEs on numerous tasks, and set new state-of-the-art results for medium-range weather prediction and post-processing ensemble weather forecasts.

A critical aspect of power systems research is the availability of suitable data, access to which is limited by privacy concerns and the sensitive nature of energy infrastructure. This lack of data, in turn, hinders the development of modern research avenues such as machine learning approaches or stochastic formulations. To overcome this challenge, this paper proposes a systematic, data-driven framework for reconstructing high-fidelity time series, using publicly-available grid snapshots and historical data published by transmission system operators. The proposed approach, from geo-spatial data and generation capacity reconstruction, to time series disaggregation, is applied to the French transmission grid. Thereby, synthetic but highly realistic time series data, spanning multiple years with a 5-minute granularity, is generated at the individual component level.

Smart home energy management systems help the distribution grid operate more efficiently and reliably, and enable effective penetration of distributed renewable energy sources. These systems rely on robust forecasting, optimization, and control/scheduling algorithms that can handle the uncertain nature of demand and renewable generation. This paper proposes an advanced ML algorithm, called Recurrent Trend Predictive Neural Network based Forecast Embedded Scheduling (rTPNN-FES), to provide efficient residential demand control. rTPNN-FES is a novel neural network architecture that simultaneously forecasts renewable energy generation and schedules household appliances. By its embedded structure, rTPNN-FES eliminates the utilization of separate algorithms for forecasting and scheduling and generates a schedule that is robust against forecasting errors. This paper also evaluates the performance of the proposed algorithm for an IoT-enabled smart home. The evaluation results reveal that rTPNN-FES provides near-optimal scheduling 37.5 times faster than the optimization while outperforming state-of-the-art forecasting techniques.

Accurate electricity load forecasting is essential for grid stability, resource optimization, and renewable energy integration. While transformer-based deep learning models like TimeGPT have gained traction in time-series forecasting, their effectiveness in long-term electricity load prediction remains uncertain. This study evaluates forecasting models ranging from classical regression techniques to advanced deep learning architectures using data from the ESD 2025 competition. The dataset includes two years of historical electricity load data, alongside temperature and global horizontal irradiance (GHI) across five sites, with a one-day-ahead forecasting horizon. Since actual test set load values remain undisclosed, leveraging predicted values would accumulate errors, making this a long-term forecasting challenge. We employ (i) Principal Component Analysis (PCA) for dimensionality reduction and (ii) frame the task as a regression problem, using temperature and GHI as covariates to predict load for each hour, (iii) ultimately stacking 24 models to generate yearly forecasts. Our results reveal that deep learning models, including TimeGPT, fail to consistently outperform simpler statistical and machine learning approaches due to the limited availability of training data and exogenous variables. In contrast, XGBoost, with minimal feature engineering, delivers the lowest error rates across all test cases while maintaining computational efficiency. This highlights the limitations of deep learning in long-term electricity forecasting and reinforces the importance of model selection based on dataset characteristics rather than complexity. Our study provides insights into practical forecasting applications and contributes to the ongoing discussion on the trade-offs between traditional and modern forecasting methods.

Traffic forecasting has emerged as a core component of intelligent transportation systems. However, timely accurate traffic forecasting, especially long-term forecasting, still remains an open challenge due to the highly nonlinear and dynamic spatial-temporal dependencies of traffic flows. In this paper, we propose a novel paradigm of Spatial-Temporal Transformer Networks (STTNs) that leverages dynamical directed spatial dependencies and long-range temporal dependencies to improve the accuracy of long-term traffic forecasting. Specifically, we present a new variant of graph neural networks, named spatial transformer, by dynamically modeling directed spatial dependencies with self-attention mechanism to capture realtime traffic conditions as well as the directionality of traffic flows. Furthermore, different spatial dependency patterns can be jointly modeled with multi-heads attention mechanism to consider diverse relationships related to different factors (e.g. similarity, connectivity and covariance). On the other hand, the temporal transformer is utilized to model long-range bidirectional temporal dependencies across multiple time steps. Finally, they are composed as a block to jointly model the spatial-temporal dependencies for accurate traffic prediction. Compared to existing works, the proposed model enables fast and scalable training over a long range spatial-temporal dependencies. Experiment results demonstrate that the proposed model achieves competitive results compared with the state-of-the-arts, especially forecasting long-term traffic flows on real-world PeMS-Bay and PeMSD7(M) datasets.

Traditional time-series forecasting often focuses only on minimizing prediction errors, ignoring the specific requirements of real-world applications that employ them. This paper presents a new training methodology, which allows a forecasting model to dynamically adjust its focus based on the importance of forecast ranges specified by the end application. Unlike previous methods that fix these ranges beforehand, our training approach breaks down predictions over the entire signal range into smaller segments, which are then dynamically weighted and combined to produce accurate forecasts. We tested our method on standard datasets, including a new dataset from wireless communication, and found that not only it improves prediction accuracy but also improves the performance of end application employing the forecasting model. This research provides a basis for creating forecasting systems that better connect prediction and decision-making in various practical applications.

Spatio-temporal forecasting is essential for real-world applications such as traffic management and urban computing. Although recent methods have shown improved accuracy, they often fail to account for dynamic deviations between current inputs and historical patterns. These deviations contain critical signals that can significantly affect model performance. To fill this gap, we propose ST-SSDL, a Spatio-Temporal time series forecasting framework that incorporates a Self-Supervised Deviation Learning scheme to capture and utilize such deviations. ST-SSDL anchors each input to its historical average and discretizes the latent space using learnable prototypes that represent typical spatio-temporal patterns. Two auxiliary objectives are proposed to refine this structure: a contrastive loss that enhances inter-prototype discriminability and a deviation loss that regularizes the distance consistency between input representations and corresponding prototypes to quantify deviation. Optimized jointly with the forecasting objective, these components guide the model to organize its hidden space and improve generalization across diverse input conditions. Experiments on six benchmark datasets show that ST-SSDL consistently outperforms state-of-the-art baselines across multiple metrics. Visualizations further demonstrate its ability to adaptively respond to varying levels of deviation in complex spatio-temporal scenarios. Our code and datasets are available at https://github.com/Jimmy-7664/ST-SSDL.

Accurate forecasting of electrical demand is essential for maintaining a stable and reliable power grid, optimizing the allocation of energy resources, and promoting efficient energy consumption practices. This study investigates the effectiveness of five hyperparameter optimization (HPO) algorithms -- Random Search, Covariance Matrix Adaptation Evolution Strategy (CMA--ES), Bayesian Optimization, Partial Swarm Optimization (PSO), and Nevergrad Optimizer (NGOpt) across univariate and multivariate Short-Term Load Forecasting (STLF) tasks. Using the Panama Electricity dataset (n=48,049), we evaluate HPO algorithms' performances on a surrogate forecasting algorithm, XGBoost, in terms of accuracy (i.e., MAPE, R^2) and runtime. Performance plots visualize these metrics across varying sample sizes from 1,000 to 20,000, and Kruskal--Wallis tests assess the statistical significance of the performance differences. Results reveal significant runtime advantages for HPO algorithms over Random Search. In univariate models, Bayesian optimization exhibited the lowest accuracy among the tested methods. This study provides valuable insights for optimizing XGBoost in the STLF context and identifies areas for future research.

Graph-based deep learning methods have become popular tools to process collections of correlated time series. Differently from traditional multivariate forecasting methods, neural graph-based predictors take advantage of pairwise relationships by conditioning forecasts on a (possibly dynamic) graph spanning the time series collection. The conditioning can take the form of an architectural inductive bias on the neural forecasting architecture, resulting in a family of deep learning models called spatiotemporal graph neural networks. Such relational inductive biases enable the training of global forecasting models on large time-series collections, while at the same time localizing predictions w.r.t. each element in the set (i.e., graph nodes) by accounting for local correlations among them (i.e., graph edges). Indeed, recent theoretical and practical advances in graph neural networks and deep learning for time series forecasting make the adoption of such processing frameworks appealing and timely. However, most of the studies in the literature focus on proposing variations of existing neural architectures by taking advantage of modern deep learning practices, while foundational and methodological aspects have not been subject to systematic investigation. To fill the gap, this paper aims to introduce a comprehensive methodological framework that formalizes the forecasting problem and provides design principles for graph-based predictive models and methods to assess their performance. At the same time, together with an overview of the field, we provide design guidelines, recommendations, and best practices, as well as an in-depth discussion of open challenges and future research directions.

Triggered by the realization that AI emulators can rival the performance of traditional numerical weather prediction models running on HPC systems, there is now an increasing number of large AI models that address use cases such as forecasting, downscaling, or nowcasting. While the parallel developments in the AI literature focus on foundation models -- models that can be effectively tuned to address multiple, different use cases -- the developments on the weather and climate side largely focus on single-use cases with particular emphasis on mid-range forecasting. We close this gap by introducing Prithvi WxC, a 2.3 billion parameter foundation model developed using 160 variables from the Modern-Era Retrospective Analysis for Research and Applications, Version 2 (MERRA-2). Prithvi WxC employs an encoder-decoder-based architecture, incorporating concepts from various recent transformer models to effectively capture both regional and global dependencies in the input data. The model has been designed to accommodate large token counts to model weather phenomena in different topologies at fine resolutions. Furthermore, it is trained with a mixed objective that combines the paradigms of masked reconstruction with forecasting. We test the model on a set of challenging downstream tasks namely: Autoregressive rollout forecasting, Downscaling, Gravity wave flux parameterization, and Extreme events estimation. The pretrained model with 2.3 billion parameters, along with the associated fine-tuning workflows, has been publicly released as an open-source contribution via Hugging Face.

Multivariate probabilistic time series forecasts are commonly evaluated via proper scoring rules, i.e., functions that are minimal in expectation for the ground-truth distribution. However, this property is not sufficient to guarantee good discrimination in the non-asymptotic regime. In this paper, we provide the first systematic finite-sample study of proper scoring rules for time-series forecasting evaluation. Through a power analysis, we identify the "region of reliability" of a scoring rule, i.e., the set of practical conditions where it can be relied on to identify forecasting errors. We carry out our analysis on a comprehensive synthetic benchmark, specifically designed to test several key discrepancies between ground-truth and forecast distributions, and we gauge the generalizability of our findings to real-world tasks with an application to an electricity production problem. Our results reveal critical shortcomings in the evaluation of multivariate probabilistic forecasts as commonly performed in the literature.

The accessibility of spatially distributed data, enabled by affordable sensors, field, and numerical experiments, has facilitated the development of data-driven solutions for scientific problems, including climate change, weather prediction, and urban planning. Neural Partial Differential Equations (Neural PDEs), which combine deep learning (DL) techniques with domain expertise (e.g., governing equations) for parameterization, have proven to be effective in capturing valuable correlations within spatiotemporal datasets. However, sparse and noisy measurements coupled with modeling approximation introduce aleatoric and epistemic uncertainties. Therefore, quantifying uncertainties propagated from model inputs to outputs remains a challenge and an essential goal for establishing the trustworthiness of Neural PDEs. This work evaluates various Uncertainty Quantification (UQ) approaches for both Forward and Inverse Problems in scientific applications. Specifically, we investigate the effectiveness of Bayesian methods, such as Hamiltonian Monte Carlo (HMC) and Monte-Carlo Dropout (MCD), and a more conventional approach, Deep Ensembles (DE). To illustrate their performance, we take two canonical PDEs: Burger's equation and the Navier-Stokes equation. Our results indicate that Neural PDEs can effectively reconstruct flow systems and predict the associated unknown parameters. However, it is noteworthy that the results derived from Bayesian methods, based on our observations, tend to display a higher degree of certainty in their predictions as compared to those obtained using the DE. This elevated certainty in predictions suggests that Bayesian techniques might underestimate the true underlying uncertainty, thereby appearing more confident in their predictions than the DE approach.

Complex, temporally evolving phenomena, from climate to brain activity, are governed by dynamical systems (DS). DS reconstruction (DSR) seeks to infer generative surrogate models of these from observed data, reproducing their long-term behavior. Existing DSR approaches require purpose-training for any new system observed, lacking the zero-shot and in-context inference capabilities known from LLMs. Here we introduce DynaMix, a novel multivariate ALRNN-based mixture-of-experts architecture pre-trained for DSR, the first DSR model able to generalize zero-shot to out-of-domain DS. Just from a provided context signal, without any re-training, DynaMix faithfully forecasts the long-term evolution of novel DS where existing time series (TS) foundation models, like Chronos, fail -- at a fraction of the number of parameters and orders of magnitude faster inference times. DynaMix outperforms TS foundation models in terms of long-term statistics, and often also short-term forecasts, even on real-world time series, like traffic or weather data, typically used for training and evaluating TS models, but not at all part of DynaMix' training corpus. We illustrate some of the failure modes of TS models for DSR problems, and conclude that models built on DS principles may bear a huge potential also for advancing the TS prediction field.

Machine learning for time-series forecasting remains a key area of research. Despite successful application of many machine learning techniques, relating computational efficiency to forecast error remains an under-explored domain. This paper addresses this topic through a series of real-time experiments to quantify the relationship between computational cost and forecast error using meteorological nowcasting as an example use-case. We employ a variety of popular regression techniques (XGBoost, FC-MLP, Transformer, and LSTM) for multi-horizon, short-term forecasting of three variables (temperature, wind speed, and cloud cover) for multiple locations. During a 5-day live experiment, 4000 data sources were streamed for training and inferencing 144 models per hour. These models were parameterized to explore forecast error for two computational cost minimization methods: a novel auto-adaptive data reduction technique (Variance Horizon) and a performance-based concept drift-detection mechanism. Forecast error of all model variations were benchmarked in real-time against a state-of-the-art numerical weather prediction model. Performance was assessed using classical and novel evaluation metrics. Results indicate that using the Variance Horizon reduced computational usage by more than 50\%, while increasing between 0-15\% in error. Meanwhile, performance-based retraining reduced computational usage by up to 90\% while also improving forecast error by up to 10\%. Finally, the combination of both the Variance Horizon and performance-based retraining outperformed other model configurations by up to 99.7\% when considering error normalized to computational usage.

The stable periodic patterns present in time series data serve as the foundation for conducting long-horizon forecasts. In this paper, we pioneer the exploration of explicitly modeling this periodicity to enhance the performance of models in long-term time series forecasting (LTSF) tasks. Specifically, we introduce the Residual Cycle Forecasting (RCF) technique, which utilizes learnable recurrent cycles to model the inherent periodic patterns within sequences, and then performs predictions on the residual components of the modeled cycles. Combining RCF with a Linear layer or a shallow MLP forms the simple yet powerful method proposed in this paper, called CycleNet. CycleNet achieves state-of-the-art prediction accuracy in multiple domains including electricity, weather, and energy, while offering significant efficiency advantages by reducing over 90% of the required parameter quantity. Furthermore, as a novel plug-and-play technique, the RCF can also significantly improve the prediction accuracy of existing models, including PatchTST and iTransformer. The source code is available at: https://github.com/ACAT-SCUT/CycleNet.

Pretrained time series models have enabled inference-only forecasting systems that produce accurate predictions without task-specific training. However, existing approaches largely focus on univariate forecasting, limiting their applicability in real-world scenarios where multivariate data and covariates play a crucial role. We present Chronos-2, a pretrained model capable of handling univariate, multivariate, and covariate-informed forecasting tasks in a zero-shot manner. Chronos-2 employs a group attention mechanism that facilitates in-context learning (ICL) through efficient information sharing across multiple time series within a group, which may represent sets of related series, variates of a multivariate series, or targets and covariates in a forecasting task. These general capabilities are achieved through training on synthetic datasets that impose diverse multivariate structures on univariate series. Chronos-2 delivers state-of-the-art performance across three comprehensive benchmarks: fev-bench, GIFT-Eval, and Chronos Benchmark II. On fev-bench, which emphasizes multivariate and covariate-informed forecasting, Chronos-2's universal ICL capabilities lead to substantial improvements over existing models. On tasks involving covariates, it consistently outperforms baselines by a wide margin. Case studies in the energy and retail domains further highlight its practical advantages. The in-context learning capabilities of Chronos-2 establish it as a general-purpose forecasting model that can be used "as is" in real-world forecasting pipelines.

Artificial Intelligence (AI) weather prediction (AIWP) models often produce "blurry" precipitation forecasts that overestimate drizzle and underestimate extremes. This study provides a novel solution to tackle this problem -- integrating terrain-following coordinates with global mass and energy conservation schemes into AIWP models. Forecast experiments are conducted to evaluate the effectiveness of this solution using FuXi, an example AIWP model, adapted to 1.0-degree grid spacing data. Verification results show large performance gains. The conservation schemes are found to reduce drizzle bias, whereas using terrain-following coordinates improves the estimation of extreme events and precipitation intensity spectra. Furthermore, a case study reveals that terrain-following coordinates capture near-surface winds better over mountains, offering AIWP models more accurate information on understanding the dynamics of precipitation processes. The proposed solution of this study can benefit a wide range of AIWP models and bring insights into how atmospheric domain knowledge can support the development of AIWP models.

The rise of accurate machine learning methods for weather forecasting is creating radical new possibilities for modeling the atmosphere. In the time of climate change, having access to high-resolution forecasts from models like these is also becoming increasingly vital. While most existing Neural Weather Prediction (NeurWP) methods focus on global forecasting, an important question is how these techniques can be applied to limited area modeling. In this work we adapt the graph-based NeurWP approach to the limited area setting and propose a multi-scale hierarchical model extension. Our approach is validated by experiments with a local model for the Nordic region.

Spatio-temporal predictive learning is a learning paradigm that enables models to learn spatial and temporal patterns by predicting future frames from given past frames in an unsupervised manner. Despite remarkable progress in recent years, a lack of systematic understanding persists due to the diverse settings, complex implementation, and difficult reproducibility. Without standardization, comparisons can be unfair and insights inconclusive. To address this dilemma, we propose OpenSTL, a comprehensive benchmark for spatio-temporal predictive learning that categorizes prevalent approaches into recurrent-based and recurrent-free models. OpenSTL provides a modular and extensible framework implementing various state-of-the-art methods. We conduct standard evaluations on datasets across various domains, including synthetic moving object trajectory, human motion, driving scenes, traffic flow and weather forecasting. Based on our observations, we provide a detailed analysis of how model architecture and dataset properties affect spatio-temporal predictive learning performance. Surprisingly, we find that recurrent-free models achieve a good balance between efficiency and performance than recurrent models. Thus, we further extend the common MetaFormers to boost recurrent-free spatial-temporal predictive learning. We open-source the code and models at https://github.com/chengtan9907/OpenSTL.

Weather nowcasting is an essential task that involves predicting future radar echo sequences based on current observations, offering significant benefits for disaster management, transportation, and urban planning. Current prediction methods are limited by training and storage efficiency, mainly focusing on 2D spatial predictions at specific altitudes. Meanwhile, 3D volumetric predictions at each timestamp remain largely unexplored. To address such a challenge, we introduce a comprehensive framework for 3D radar sequence prediction in weather nowcasting, using the newly proposed SpatioTemporal Coherent Gaussian Splatting (STC-GS) for dynamic radar representation and GauMamba for efficient and accurate forecasting. Specifically, rather than relying on a 4D Gaussian for dynamic scene reconstruction, STC-GS optimizes 3D scenes at each frame by employing a group of Gaussians while effectively capturing their movements across consecutive frames. It ensures consistent tracking of each Gaussian over time, making it particularly effective for prediction tasks. With the temporally correlated Gaussian groups established, we utilize them to train GauMamba, which integrates a memory mechanism into the Mamba framework. This allows the model to learn the temporal evolution of Gaussian groups while efficiently handling a large volume of Gaussian tokens. As a result, it achieves both efficiency and accuracy in forecasting a wide range of dynamic meteorological radar signals. The experimental results demonstrate that our STC-GS can efficiently represent 3D radar sequences with over 16times higher spatial resolution compared with the existing 3D representation methods, while GauMamba outperforms state-of-the-art methods in forecasting a broad spectrum of high-dynamic weather conditions.

Multivariate time series forecasting is an important machine learning problem across many domains, including predictions of solar plant energy output, electricity consumption, and traffic jam situation. Temporal data arise in these real-world applications often involves a mixture of long-term and short-term patterns, for which traditional approaches such as Autoregressive models and Gaussian Process may fail. In this paper, we proposed a novel deep learning framework, namely Long- and Short-term Time-series network (LSTNet), to address this open challenge. LSTNet uses the Convolution Neural Network (CNN) and the Recurrent Neural Network (RNN) to extract short-term local dependency patterns among variables and to discover long-term patterns for time series trends. Furthermore, we leverage traditional autoregressive model to tackle the scale insensitive problem of the neural network model. In our evaluation on real-world data with complex mixtures of repetitive patterns, LSTNet achieved significant performance improvements over that of several state-of-the-art baseline methods. All the data and experiment codes are available online.

Accurate traffic forecasting is challenging due to the complex dependency on road networks, various types of roads, and the abrupt speed change due to the events. Recent works mainly focus on dynamic spatial modeling with adaptive graph embedding or graph attention having less consideration for temporal characteristics and in-situ modeling. In this paper, we propose a novel deep learning model named TESTAM, which individually models recurring and non-recurring traffic patterns by a mixture-of-experts model with three experts on temporal modeling, spatio-temporal modeling with static graph, and dynamic spatio-temporal dependency modeling with dynamic graph. By introducing different experts and properly routing them, TESTAM could better model various circumstances, including spatially isolated nodes, highly related nodes, and recurring and non-recurring events. For the proper routing, we reformulate a gating problem into a classification problem with pseudo labels. Experimental results on three public traffic network datasets, METR-LA, PEMS-BAY, and EXPY-TKY, demonstrate that TESTAM achieves a better indication and modeling of recurring and non-recurring traffic. We published the official code at https://github.com/HyunWookL/TESTAM

While complex simulations of physical systems have been widely used in engineering and scientific computing, lowering their often prohibitive computational requirements has only recently been tackled by deep learning approaches. In this paper, we present GraphSplineNets, a novel deep-learning method to speed up the forecasting of physical systems by reducing the grid size and number of iteration steps of deep surrogate models. Our method uses two differentiable orthogonal spline collocation methods to efficiently predict response at any location in time and space. Additionally, we introduce an adaptive collocation strategy in space to prioritize sampling from the most important regions. GraphSplineNets improve the accuracy-speedup tradeoff in forecasting various dynamical systems with increasing complexity, including the heat equation, damped wave propagation, Navier-Stokes equations, and real-world ocean currents in both regular and irregular domains.

In this paper, we present Pangu-Weather, a deep learning based system for fast and accurate global weather forecast. For this purpose, we establish a data-driven environment by downloading 43 years of hourly global weather data from the 5th generation of ECMWF reanalysis (ERA5) data and train a few deep neural networks with about 256 million parameters in total. The spatial resolution of forecast is 0.25^circtimes0.25^circ, comparable to the ECMWF Integrated Forecast Systems (IFS). More importantly, for the first time, an AI-based method outperforms state-of-the-art numerical weather prediction (NWP) methods in terms of accuracy (latitude-weighted RMSE and ACC) of all factors (e.g., geopotential, specific humidity, wind speed, temperature, etc.) and in all time ranges (from one hour to one week). There are two key strategies to improve the prediction accuracy: (i) designing a 3D Earth Specific Transformer (3DEST) architecture that formulates the height (pressure level) information into cubic data, and (ii) applying a hierarchical temporal aggregation algorithm to alleviate cumulative forecast errors. In deterministic forecast, Pangu-Weather shows great advantages for short to medium-range forecast (i.e., forecast time ranges from one hour to one week). Pangu-Weather supports a wide range of downstream forecast scenarios, including extreme weather forecast (e.g., tropical cyclone tracking) and large-member ensemble forecast in real-time. Pangu-Weather not only ends the debate on whether AI-based methods can surpass conventional NWP methods, but also reveals novel directions for improving deep learning weather forecast systems.

Multivariate time series forecasting is essential in domains such as finance, transportation, climate, and energy. However, existing patch-based methods typically adopt fixed-length segmentation, overlooking the heterogeneity of local temporal dynamics and the decoding heterogeneity of forecasting. Such designs lose details in information-dense regions, introduce redundancy in stable segments, and fail to capture the distinct complexities of short-term and long-term horizons. We propose TimeMosaic, a forecasting framework that aims to address temporal heterogeneity. TimeMosaic employs adaptive patch embedding to dynamically adjust granularity according to local information density, balancing motif reuse with structural clarity while preserving temporal continuity. In addition, it introduces segment-wise decoding that treats each prediction horizon as a related subtask and adapts to horizon-specific difficulty and information requirements, rather than applying a single uniform decoder. Extensive evaluations on benchmark datasets demonstrate that TimeMosaic delivers consistent improvements over existing methods, and our model trained on the large-scale corpus with 321 billion observations achieves performance competitive with state-of-the-art TSFMs.

Multivariate time series is prevalent in many scientific and industrial domains. Modeling multivariate signals is challenging due to their long-range temporal dependencies and intricate interactions--both direct and indirect. To confront these complexities, we introduce a method of representing multivariate signals as nodes in a graph with edges indicating interdependency between them. Specifically, we leverage graph neural networks (GNN) and attention mechanisms to efficiently learn the underlying relationships within the time series data. Moreover, we suggest employing hierarchical signal decompositions running over the graphs to capture multiple spatial dependencies. The effectiveness of our proposed model is evaluated across various real-world benchmark datasets designed for long-term forecasting tasks. The results consistently showcase the superiority of our model, achieving an average 23\% reduction in mean squared error (MSE) compared to existing models.

Accurate probabilistic weather forecasting demands both high accuracy and efficient uncertainty quantification, challenges that overburden both ensemble numerical weather prediction (NWP) and recent machine-learning methods. We introduce LaDCast, the first global latent-diffusion framework for medium-range ensemble forecasting, which generates hourly ensemble forecasts entirely in a learned latent space. An autoencoder compresses high-dimensional ERA5 reanalysis fields into a compact representation, and a transformer-based diffusion model produces sequential latent updates with arbitrary hour initialization. The model incorporates Geometric Rotary Position Embedding (GeoRoPE) to account for the Earth's spherical geometry, a dual-stream attention mechanism for efficient conditioning, and sinusoidal temporal embeddings to capture seasonal patterns. LaDCast achieves deterministic and probabilistic skill close to that of the European Centre for Medium-Range Forecast IFS-ENS, without any explicit perturbations. Notably, LaDCast demonstrates superior performance in tracking rare extreme events such as cyclones, capturing their trajectories more accurately than established models. By operating in latent space, LaDCast reduces storage and compute by orders of magnitude, demonstrating a practical path toward forecasting at kilometer-scale resolution in real time. We open-source our code and models and provide the training and evaluation pipelines at: https://github.com/tonyzyl/ladcast.

Weather forecasting is critical for a range of human activities including transportation, agriculture, industry, as well as the safety of the general public. Machine learning models have the potential to transform the complex weather prediction pipeline, but current approaches still rely on numerical weather prediction (NWP) systems, limiting forecast speed and accuracy. Here we demonstrate that a machine learning model can replace the entire operational NWP pipeline. Aardvark Weather, an end-to-end data-driven weather prediction system, ingests raw observations and outputs global gridded forecasts and local station forecasts. Further, it can be optimised end-to-end to maximise performance over quantities of interest. Global forecasts outperform an operational NWP baseline for multiple variables and lead times. Local station forecasts are skillful up to ten days lead time and achieve comparable and often lower errors than a post-processed global NWP baseline and a state-of-the-art end-to-end forecasting system with input from human forecasters. These forecasts are produced with a remarkably simple neural process model using just 8% of the input data and three orders of magnitude less compute than existing NWP and hybrid AI-NWP methods. We anticipate that Aardvark Weather will be the starting point for a new generation of end-to-end machine learning models for medium-range forecasting that will reduce computational costs by orders of magnitude and enable the rapid and cheap creation of bespoke models for users in a variety of fields, including for the developing world where state-of-the-art local models are not currently available.

Generative models have demonstrated remarkable success in domains such as text, image, and video synthesis. In this work, we explore the application of generative models to fluid dynamics, specifically for turbulence simulation, where classical numerical solvers are computationally expensive. We propose a novel stochastic generative model based on stochastic interpolants, which enables probabilistic forecasting while incorporating physical constraints such as energy stability and divergence-freeness. Unlike conventional stochastic generative models, which are often agnostic to underlying physical laws, our approach embeds energy consistency by making the parameters of the stochastic interpolant learnable coefficients. We evaluate our method on a benchmark turbulence problem - Kolmogorov flow - demonstrating superior accuracy and stability over state-of-the-art alternatives such as autoregressive conditional diffusion models (ACDMs) and PDE-Refiner. Furthermore, we achieve stable results for significantly longer roll-outs than standard stochastic interpolants. Our results highlight the potential of physics-aware generative models in accelerating and enhancing turbulence simulations while preserving fundamental conservation properties.

We present a novel framework for motion forecasting with Dual Consistency Constraints and Multi-Pseudo-Target supervision. The motion forecasting task predicts future trajectories of vehicles by incorporating spatial and temporal information from the past. A key design of DCMS is the proposed Dual Consistency Constraints that regularize the predicted trajectories under spatial and temporal perturbation during the training stage. In addition, we design a novel self-ensembling scheme to obtain accurate pseudo targets to model the multi-modality in motion forecasting through supervision with multiple targets explicitly, namely Multi-Pseudo-Target supervision. Our experimental results on the Argoverse motion forecasting benchmark show that DCMS significantly outperforms the state-of-the-art methods, achieving 1st place on the leaderboard. We also demonstrate that our proposed strategies can be incorporated into other motion forecasting approaches as general training schemes.

Climate and weather prediction traditionally relies on complex numerical simulations of atmospheric physics. Deep learning approaches, such as transformers, have recently challenged the simulation paradigm with complex network forecasts. However, they often act as data-driven black-box models that neglect the underlying physics and lack uncertainty quantification. We address these limitations with ClimODE, a spatiotemporal continuous-time process that implements a key principle of advection from statistical mechanics, namely, weather changes due to a spatial movement of quantities over time. ClimODE models precise weather evolution with value-conserving dynamics, learning global weather transport as a neural flow, which also enables estimating the uncertainty in predictions. Our approach outperforms existing data-driven methods in global and regional forecasting with an order of magnitude smaller parameterization, establishing a new state of the art.

Accurate prediction of climate in the subseasonal-to-seasonal scale is crucial for disaster readiness, reduced economic risk, and improved policy-making amidst climate change. Yet, S2S prediction remains challenging due to the chaotic nature of the system. At present, existing benchmarks for weather and climate applications, tend to (1) have shorter forecasting range of up-to 14 days, (2) do not include a wide range of operational baseline forecasts, and (3) lack physics-based constraints for explainability. Thus, we propose ChaosBench, a large-scale, multi-channel, physics-based benchmark for S2S prediction. ChaosBench has over 460K frames of real-world observations and simulations, each with 60 variable-channels and spanning for up-to 45 years. We also propose several physics-based, in addition to vision-based metrics, that enables for a more physically-consistent model. Furthermore, we include a diverse set of physics-based forecasts from 4 national weather agencies as baselines to our data-driven counterpart. We establish two tasks that vary in complexity: full and sparse dynamics prediction. Our benchmark is one of the first to perform large-scale evaluation on existing models including PanguWeather, FourCastNetV2, GraphCast, and ClimaX, and finds methods originally developed for weather-scale applications fails on S2S task. We release our benchmark code and datasets at https://leap-stc.github.io/ChaosBench.

Forecasting on sparse multivariate time series (MTS) aims to model the predictors of future values of time series given their incomplete past, which is important for many emerging applications. However, most existing methods process MTS's individually, and do not leverage the dynamic distributions underlying the MTS's, leading to sub-optimal results when the sparsity is high. To address this challenge, we propose a novel generative model, which tracks the transition of latent clusters, instead of isolated feature representations, to achieve robust modeling. It is characterized by a newly designed dynamic Gaussian mixture distribution, which captures the dynamics of clustering structures, and is used for emitting timeseries. The generative model is parameterized by neural networks. A structured inference network is also designed for enabling inductive analysis. A gating mechanism is further introduced to dynamically tune the Gaussian mixture distributions. Extensive experimental results on a variety of real-life datasets demonstrate the effectiveness of our method.

Probabilistic forecasting is crucial to decision-making under uncertainty about future weather. The dominant approach is to use an ensemble of forecasts to represent and quantify uncertainty in operational numerical weather prediction. However, generating ensembles is computationally costly. In this paper, we propose to generate ensemble forecasts at scale by leveraging recent advances in generative artificial intelligence. Our approach learns a data-driven probabilistic diffusion model from the 5-member ensemble GEFS reforecast dataset. The model can then be sampled efficiently to produce realistic weather forecasts, conditioned on a few members of the operational GEFS forecasting system. The generated ensembles have similar predictive skill as the full GEFS 31-member ensemble, evaluated against ERA5 reanalysis, and emulate well the statistics of large physics-based ensembles. We also apply the same methodology to developing a diffusion model for generative post-processing: the model directly learns to correct biases present in the emulated forecasting system by leveraging reanalysis data as labels during training. Ensembles from this generative post-processing model show greater reliability and accuracy, particularly in extreme event classification. In general, they are more reliable and forecast the probability of extreme weather more accurately than the GEFS operational ensemble. Our models achieve these results at less than 1/10th of the computational cost incurred by the operational GEFS system.

Weather forecasts are fundamentally uncertain, so predicting the range of probable weather scenarios is crucial for important decisions, from warning the public about hazardous weather, to planning renewable energy use. Here, we introduce GenCast, a probabilistic weather model with greater skill and speed than the top operational medium-range weather forecast in the world, the European Centre for Medium-Range Forecasts (ECMWF)'s ensemble forecast, ENS. Unlike traditional approaches, which are based on numerical weather prediction (NWP), GenCast is a machine learning weather prediction (MLWP) method, trained on decades of reanalysis data. GenCast generates an ensemble of stochastic 15-day global forecasts, at 12-hour steps and 0.25 degree latitude-longitude resolution, for over 80 surface and atmospheric variables, in 8 minutes. It has greater skill than ENS on 97.4% of 1320 targets we evaluated, and better predicts extreme weather, tropical cyclones, and wind power production. This work helps open the next chapter in operational weather forecasting, where critical weather-dependent decisions are made with greater accuracy and efficiency.

Accurate spatial-temporal traffic flow forecasting is crucial in aiding traffic managers in implementing control measures and assisting drivers in selecting optimal travel routes. Traditional deep-learning based methods for traffic flow forecasting typically rely on historical data to train their models, which are then used to make predictions on future data. However, the performance of the trained model usually degrades due to the temporal drift between the historical and future data. To make the model trained on historical data better adapt to future data in a fully online manner, this paper conducts the first study of the online test-time adaptation techniques for spatial-temporal traffic flow forecasting problems. To this end, we propose an Adaptive Double Correction by Series Decomposition (ADCSD) method, which first decomposes the output of the trained model into seasonal and trend-cyclical parts and then corrects them by two separate modules during the testing phase using the latest observed data entry by entry. In the proposed ADCSD method, instead of fine-tuning the whole trained model during the testing phase, a lite network is attached after the trained model, and only the lite network is fine-tuned in the testing process each time a data entry is observed. Moreover, to satisfy that different time series variables may have different levels of temporal drift, two adaptive vectors are adopted to provide different weights for different time series variables. Extensive experiments on four real-world traffic flow forecasting datasets demonstrate the effectiveness of the proposed ADCSD method. The code is available at https://github.com/Pengxin-Guo/ADCSD.

In recent years, diffusion models have emerged as powerful tools for generating ensemble members in meteorology. In this work, we demonstrate that a Denoising Diffusion Implicit Model (DDIM) can effectively control ensemble variance by varying the number of diffusion steps. Introducing a theoretical framework, we relate diffusion steps to the variance expressed by the reverse diffusion process. Focusing on reanalysis downscaling, we propose an ensemble diffusion model for the full ERA5-to-CERRA domain, generating variance-calibrated ensemble members for wind speed at full spatial and temporal resolution. Our method aligns global mean variance with a reference ensemble dataset and ensures spatial variance is distributed in accordance with observed meteorological variability. Additionally, we address the lack of ensemble information in the CARRA dataset, showcasing the utility of our approach for efficient, high-resolution ensemble generation.

Air pollution remains a leading global health risk, exacerbated by rapid industrialization and urbanization, contributing significantly to morbidity and mortality rates. In this paper, we introduce AirCast, a novel multi-variable air pollution forecasting model, by combining weather and air quality variables. AirCast employs a multi-task head architecture that simultaneously forecasts atmospheric conditions and pollutant concentrations, improving its understanding of how weather patterns affect air quality. Predicting extreme pollution events is challenging due to their rare occurrence in historic data, resulting in a heavy-tailed distribution of pollution levels. To address this, we propose a novel Frequency-weighted Mean Absolute Error (fMAE) loss, adapted from the class-balanced loss for regression tasks. Informed from domain knowledge, we investigate the selection of key variables known to influence pollution levels. Additionally, we align existing weather and chemical datasets across spatial and temporal dimensions. AirCast's integrated approach, combining multi-task learning, frequency weighted loss and domain informed variable selection, enables more accurate pollution forecasts. Our source code and models are made public here (https://github.com/vishalned/AirCast.git)

Data-driven deep learning models are transforming global weather forecasting. It is an open question if this success can extend to climate modeling, where the complexity of the data and long inference rollouts pose significant challenges. Here, we present the first conditional generative model that produces accurate and physically consistent global climate ensemble simulations by emulating a coarse version of the United States' primary operational global forecast model, FV3GFS. Our model integrates the dynamics-informed diffusion framework (DYffusion) with the Spherical Fourier Neural Operator (SFNO) architecture, enabling stable 100-year simulations at 6-hourly timesteps while maintaining low computational overhead compared to single-step deterministic baselines. The model achieves near gold-standard performance for climate model emulation, outperforming existing approaches and demonstrating promising ensemble skill. This work represents a significant advance towards efficient, data-driven climate simulations that can enhance our understanding of the climate system and inform adaptation strategies.

The maritime industry's continuous commitment to sustainability has led to a dedicated exploration of methods to reduce vessel fuel consumption. This paper undertakes this challenge through a machine learning approach, leveraging a real-world dataset spanning two years of a ferry in west coast Canada. Our focus centers on the creation of a time series forecasting model given the dynamic and static states, actions, and disturbances. This model is designed to predict dynamic states based on the actions provided, subsequently serving as an evaluative tool to assess the proficiency of the ferry's operation under the captain's guidance. Additionally, it lays the foundation for future optimization algorithms, providing valuable feedback on decision-making processes. To facilitate future studies, our code is available at https://github.com/pagand/model_optimze_vessel/tree/AAAI

We present GeoGrid-Bench, a benchmark designed to evaluate the ability of foundation models to understand geo-spatial data in the grid structure. Geo-spatial datasets pose distinct challenges due to their dense numerical values, strong spatial and temporal dependencies, and unique multimodal representations including tabular data, heatmaps, and geographic visualizations. To assess how foundation models can support scientific research in this domain, GeoGrid-Bench features large-scale, real-world data covering 16 climate variables across 150 locations and extended time frames. The benchmark includes approximately 3,200 question-answer pairs, systematically generated from 8 domain expert-curated templates to reflect practical tasks encountered by human scientists. These range from basic queries at a single location and time to complex spatiotemporal comparisons across regions and periods. Our evaluation reveals that vision-language models perform best overall, and we provide a fine-grained analysis of the strengths and limitations of different foundation models in different geo-spatial tasks. This benchmark offers clearer insights into how foundation models can be effectively applied to geo-spatial data analysis and used to support scientific research.

We present a novel approach for traffic forecasting in urban traffic scenarios using a combination of spectral graph analysis and deep learning. We predict both the low-level information (future trajectories) as well as the high-level information (road-agent behavior) from the extracted trajectory of each road-agent. Our formulation represents the proximity between the road agents using a weighted dynamic geometric graph (DGG). We use a two-stream graph-LSTM network to perform traffic forecasting using these weighted DGGs. The first stream predicts the spatial coordinates of road-agents, while the second stream predicts whether a road-agent is going to exhibit overspeeding, underspeeding, or neutral behavior by modeling spatial interactions between road-agents. Additionally, we propose a new regularization algorithm based on spectral clustering to reduce the error margin in long-term prediction (3-5 seconds) and improve the accuracy of the predicted trajectories. Moreover, we prove a theoretical upper bound on the regularized prediction error. We evaluate our approach on the Argoverse, Lyft, Apolloscape, and NGSIM datasets and highlight the benefits over prior trajectory prediction methods. In practice, our approach reduces the average prediction error by approximately 75% over prior algorithms and achieves a weighted average accuracy of 91.2% for behavior prediction. Additionally, our spectral regularization improves long-term prediction by up to 70%.

Ensemble forecasting is crucial for improving weather predictions, especially for forecasts of extreme events. Constructing an ensemble prediction system (EPS) based on conventional NWP models is highly computationally expensive. ML models have emerged as valuable tools for deterministic weather forecasts, providing forecasts with significantly reduced computational requirements and even surpassing the forecast performance of traditional NWP models. However, challenges arise when applying ML models to ensemble forecasting. Recent ML models, such as GenCast and SEEDS model, rely on the ERA5 EDA or operational NWP ensemble members for forecast generation. Their spatial resolution is also considered too coarse for many applications. To overcome these limitations, we introduce FuXi-ENS, an advanced ML model designed to deliver 6-hourly global ensemble weather forecasts up to 15 days. This model runs at a significantly increased spatial resolution of 0.25\textdegree, incorporating 5 atmospheric variables at 13 pressure levels, along with 13 surface variables. By leveraging the inherent probabilistic nature of Variational AutoEncoder (VAE), FuXi-ENS optimizes a loss function that combines the CRPS and the KL divergence between the predicted and target distribution, facilitating the incorporation of flow-dependent perturbations in both initial conditions and forecast. This innovative approach makes FuXi-ENS an advancement over the traditional ones that use L1 loss combined with the KL loss in standard VAE models for ensemble weather forecasting. Results demonstrate that FuXi-ENS outperforms ensemble forecasts from the ECMWF, a world leading NWP model, in the CRPS of 98.1% of 360 variable and forecast lead time combinations. This achievement underscores the potential of the FuXi-ENS model to enhance ensemble weather forecasts, offering a promising direction for further development in this field.

Global climate models typically operate at a grid resolution of hundreds of kilometers and fail to resolve atmospheric mesoscale processes, e.g., clouds, precipitation, and gravity waves (GWs). Model representation of these processes and their sources is essential to the global circulation and planetary energy budget, but subgrid scale contributions from these processes are often only approximately represented in models using parameterizations. These parameterizations are subject to approximations and idealizations, which limit their capability and accuracy. The most drastic of these approximations is the "single-column approximation" which completely neglects the horizontal evolution of these processes, resulting in key biases in current climate models. With a focus on atmospheric GWs, we present the first-ever global simulation of atmospheric GW fluxes using machine learning (ML) models trained on the WINDSET dataset to emulate global GW emulation in the atmosphere, as an alternative to traditional single-column parameterizations. Using an Attention U-Net-based architecture trained on globally resolved GW momentum fluxes, we illustrate the importance and effectiveness of global nonlocality, when simulating GWs using data-driven schemes.

An accurate solar wind speed model is important for space weather predictions, catastrophic event warnings, and other issues concerning solar wind - magnetosphere interaction. In this work, we construct a model based on convolutional neural network (CNN) and Potential Field Source Surface (PFSS) magnetograms, considering a solar wind source surface of R_{rm SS}=2.5R_odot, aiming to predict the solar wind speed at the Lagrange 1 (L1) point of the Sun-Earth system. The input of our model consists of four Potential Field Source Surface (PFSS) magnetograms at R_{rm SS}, which are 7, 6, 5, and 4 days before the target epoch. Reduced magnetograms are used to promote the model's efficiency. We use the Global Oscillation Network Group (GONG) photospheric magnetograms and the potential field extrapolation model to generate PFSS magnetograms at the source surface. The model provides predictions of the continuous test dataset with an averaged correlation coefficient (CC) of 0.52 and a root mean square error (RMSE) of 80.8 km/s in an eight-fold validation training scheme with the time resolution of the data as small as one hour. The model also has the potential to forecast high speed streams of the solar wind, which can be quantified with a general threat score of 0.39.

The ever-increasing sensor service, though opening a precious path and providing a deluge of earth system data for deep-learning-oriented earth science, sadly introduce a daunting obstacle to their industrial level deployment. Concretely, earth science systems rely heavily on the extensive deployment of sensors, however, the data collection from sensors is constrained by complex geographical and social factors, making it challenging to achieve comprehensive coverage and uniform deployment. To alleviate the obstacle, traditional approaches to sensor deployment utilize specific algorithms to design and deploy sensors. These methods dynamically adjust the activation times of sensors to optimize the detection process across each sub-region. Regrettably, formulating an activation strategy generally based on historical observations and geographic characteristics, which make the methods and resultant models were neither simple nor practical. Worse still, the complex technical design may ultimately lead to a model with weak generalizability. In this paper, we introduce for the first time the concept of spatio-temporal data dynamic sparse training and are committed to adaptively, dynamically filtering important sensor distributions. To our knowledge, this is the first proposal (termed DynST) of an industry-level deployment optimization concept at the data level. However, due to the existence of the temporal dimension, pruning of spatio-temporal data may lead to conflicts at different timestamps. To achieve this goal, we employ dynamic merge technology, along with ingenious dimensional mapping to mitigate potential impacts caused by the temporal aspect. During the training process, DynST utilize iterative pruning and sparse training, repeatedly identifying and dynamically removing sensor perception areas that contribute the least to future predictions.

As deep learning technology advances and more urban spatial-temporal data accumulates, an increasing number of deep learning models are being proposed to solve urban spatial-temporal prediction problems. However, there are limitations in the existing field, including open-source data being in various formats and difficult to use, few papers making their code and data openly available, and open-source models often using different frameworks and platforms, making comparisons challenging. A standardized framework is urgently needed to implement and evaluate these methods. To address these issues, we propose LibCity, an open-source library that offers researchers a credible experimental tool and a convenient development framework. In this library, we have reproduced 65 spatial-temporal prediction models and collected 55 spatial-temporal datasets, allowing researchers to conduct comprehensive experiments conveniently. By enabling fair model comparisons, designing a unified data storage format, and simplifying the process of developing new models, LibCity is poised to make significant contributions to the spatial-temporal prediction field.

This paper presents a machine-learning study for solar inverter power regulation in a remote microgrid. Machine learning models for active and reactive power control are respectively trained using an ensemble learning method. Then, unlike conventional schemes that make inferences on a central server in the far-end control center, the proposed scheme deploys the trained models on an embedded edge-computing device near the inverter to reduce the communication delay. Experiments on a real embedded device achieve matched results as on the desktop PC, with about 0.1ms time cost for each inference input.

This paper presents OLinear, a linear-based multivariate time series forecasting model that operates in an orthogonally transformed domain. Recent forecasting models typically adopt the temporal forecast (TF) paradigm, which directly encode and decode time series in the time domain. However, the entangled step-wise dependencies in series data can hinder the performance of TF. To address this, some forecasters conduct encoding and decoding in the transformed domain using fixed, dataset-independent bases (e.g., sine and cosine signals in the Fourier transform). In contrast, we utilize OrthoTrans, a data-adaptive transformation based on an orthogonal matrix that diagonalizes the series' temporal Pearson correlation matrix. This approach enables more effective encoding and decoding in the decorrelated feature domain and can serve as a plug-in module to enhance existing forecasters. To enhance the representation learning for multivariate time series, we introduce a customized linear layer, NormLin, which employs a normalized weight matrix to capture multivariate dependencies. Empirically, the NormLin module shows a surprising performance advantage over multi-head self-attention, while requiring nearly half the FLOPs. Extensive experiments on 24 benchmarks and 140 forecasting tasks demonstrate that OLinear consistently achieves state-of-the-art performance with high efficiency. Notably, as a plug-in replacement for self-attention, the NormLin module consistently enhances Transformer-based forecasters. The code and datasets are available at https://anonymous.4open.science/r/OLinear

We present a data-driven approach for forecasting global weather using graph neural networks. The system learns to step forward the current 3D atmospheric state by six hours, and multiple steps are chained together to produce skillful forecasts going out several days into the future. The underlying model is trained on reanalysis data from ERA5 or forecast data from GFS. Test performance on metrics such as Z500 (geopotential height) and T850 (temperature) improves upon previous data-driven approaches and is comparable to operational, full-resolution, physical models from GFS and ECMWF, at least when evaluated on 1-degree scales and when using reanalysis initial conditions. We also show results from connecting this data-driven model to live, operational forecasts from GFS.

This paper investigates the potential privacy risks associated with forecasting models, with specific emphasis on their application in the context of smart grids. While machine learning and deep learning algorithms offer valuable utility, concerns arise regarding their exposure of sensitive information. Previous studies have focused on classification models, overlooking risks associated with forecasting models. Deep learning based forecasting models, such as Long Short Term Memory (LSTM), play a crucial role in several applications including optimizing smart grid systems but also introduce privacy risks. Our study analyzes the ability of forecasting models to leak global properties and privacy threats in smart grid systems. We demonstrate that a black box access to an LSTM model can reveal a significant amount of information equivalent to having access to the data itself (with the difference being as low as 1% in Area Under the ROC Curve). This highlights the importance of protecting forecasting models at the same level as the data.

Forecasting surface water dynamics is crucial for water resource management and climate change adaptation. However, the field lacks comprehensive datasets and standardized benchmarks. In this paper, we introduce HydroChronos, a large-scale, multi-modal spatiotemporal dataset for surface water dynamics forecasting designed to address this gap. We couple the dataset with three forecasting tasks. The dataset includes over three decades of aligned Landsat 5 and Sentinel-2 imagery, climate data, and Digital Elevation Models for diverse lakes and rivers across Europe, North America, and South America. We also propose AquaClimaTempo UNet, a novel spatiotemporal architecture with a dedicated climate data branch, as a strong benchmark baseline. Our model significantly outperforms a Persistence baseline for forecasting future water dynamics by +14% and +11% F1 across change detection and direction of change classification tasks, and by +0.1 MAE on the magnitude of change regression. Finally, we conduct an Explainable AI analysis to identify the key climate variables and input channels that influence surface water change, providing insights to inform and guide future modeling efforts.

Price responsiveness is a major feature of end use customers (EUCs) that participate in demand response (DR) programs, and has been conventionally modeled with static demand functions, which take the electricity price as the input and the aggregate energy consumption as the output. This, however, neglects the inherent temporal correlation of the EUC behaviors, and may result in large errors when predicting the actual responses of EUCs in real-time pricing (RTP) programs. In this paper, we propose a dynamical DR model so as to capture the temporal behavior of the EUCs. The states in the proposed dynamical DR model can be explicitly chosen, in which case the model can be represented by a linear function or a multi-layer feedforward neural network, or implicitly chosen, in which case the model can be represented by a recurrent neural network or a long short-term memory unit network. In both cases, the dynamical DR model can be learned from historical price and energy consumption data. Numerical simulation illustrated how the states are chosen and also showed the proposed dynamical DR model significantly outperforms the static ones.

Most state-of-the-art approaches for weather and climate modeling are based on physics-informed numerical models of the atmosphere. These approaches aim to model the non-linear dynamics and complex interactions between multiple variables, which are challenging to approximate. Additionally, many such numerical models are computationally intensive, especially when modeling the atmospheric phenomenon at a fine-grained spatial and temporal resolution. Recent data-driven approaches based on machine learning instead aim to directly solve a downstream forecasting or projection task by learning a data-driven functional mapping using deep neural networks. However, these networks are trained using curated and homogeneous climate datasets for specific spatiotemporal tasks, and thus lack the generality of numerical models. We develop and demonstrate ClimaX, a flexible and generalizable deep learning model for weather and climate science that can be trained using heterogeneous datasets spanning different variables, spatio-temporal coverage, and physical groundings. ClimaX extends the Transformer architecture with novel encoding and aggregation blocks that allow effective use of available compute while maintaining general utility. ClimaX is pre-trained with a self-supervised learning objective on climate datasets derived from CMIP6. The pre-trained ClimaX can then be fine-tuned to address a breadth of climate and weather tasks, including those that involve atmospheric variables and spatio-temporal scales unseen during pretraining. Compared to existing data-driven baselines, we show that this generality in ClimaX results in superior performance on benchmarks for weather forecasting and climate projections, even when pretrained at lower resolutions and compute budgets.

Air quality prediction and modelling plays a pivotal role in public health and environment management, for individuals and authorities to make informed decisions. Although traditional data-driven models have shown promise in this domain, their long-term prediction accuracy can be limited, especially in scenarios with sparse or incomplete data and they often rely on black-box deep learning structures that lack solid physical foundation leading to reduced transparency and interpretability in predictions. To address these limitations, this paper presents a novel approach named Physics guided Neural Network for Air Quality Prediction (AirPhyNet). Specifically, we leverage two well-established physics principles of air particle movement (diffusion and advection) by representing them as differential equation networks. Then, we utilize a graph structure to integrate physics knowledge into a neural network architecture and exploit latent representations to capture spatio-temporal relationships within the air quality data. Experiments on two real-world benchmark datasets demonstrate that AirPhyNet outperforms state-of-the-art models for different testing scenarios including different lead time (24h, 48h, 72h), sparse data and sudden change prediction, achieving reduction in prediction errors up to 10%. Moreover, a case study further validates that our model captures underlying physical processes of particle movement and generates accurate predictions with real physical meaning.

Renewable energy forecasting is attaining greater importance due to its constant increase in contribution to the electrical power grids. Solar energy is one of the most significant contributors to renewable energy and is dependent on solar irradiation. For the effective management of electrical power grids, forecasting models that predict solar irradiation, with high accuracy, are needed. In the current study, Machine Learning techniques such as Linear Regression, Extreme Gradient Boosting and Genetic Algorithm Optimization are used to forecast solar irradiation. The data used for training and validation is recorded from across three different geographical stations in the United States that are part of the SURFRAD network. A Global Horizontal Index (GHI) is predicted for the models built and compared. Genetic Algorithm Optimization is applied to XGB to further improve the accuracy of solar irradiation prediction.

Recent efforts have been dedicated to enhancing time series forecasting accuracy by introducing advanced network architectures and self-supervised pretraining strategies. Nevertheless, existing approaches still exhibit two critical drawbacks. Firstly, these methods often rely on a single dataset for training, limiting the model's generalizability due to the restricted scale of the training data. Secondly, the one-step generation schema is widely followed, which necessitates a customized forecasting head and overlooks the temporal dependencies in the output series, and also leads to increased training costs under different horizon length settings. To address these issues, we propose a novel generative pretrained hierarchical transformer architecture for forecasting, named GPHT. There are two aspects of key designs in GPHT. On the one hand, we advocate for constructing a mixed dataset for pretraining our model, comprising various datasets from diverse data scenarios. This approach significantly expands the scale of training data, allowing our model to uncover commonalities in time series data and facilitating improved transfer to specific datasets. On the other hand, GPHT employs an auto-regressive forecasting approach under the channel-independent assumption, effectively modeling temporal dependencies in the output series. Importantly, no customized forecasting head is required, enabling a single model to forecast at arbitrary horizon settings. We conduct sufficient experiments on eight datasets with mainstream self-supervised pretraining models and supervised models. The results demonstrated that GPHT surpasses the baseline models across various fine-tuning and zero/few-shot learning settings in the traditional long-term forecasting task, providing support for verifying the feasibility of pretrained time series large models.

The atmosphere affects humans in a multitude of ways, from loss of life due to adverse weather effects to long-term social and economic impacts on societies. Computer simulations of atmospheric dynamics are, therefore, of great importance for the well-being of our and future generations. Here, we propose AtmoRep, a novel, task-independent stochastic computer model of atmospheric dynamics that can provide skillful results for a wide range of applications. AtmoRep uses large-scale representation learning from artificial intelligence to determine a general description of the highly complex, stochastic dynamics of the atmosphere from the best available estimate of the system's historical trajectory as constrained by observations. This is enabled by a novel self-supervised learning objective and a unique ensemble that samples from the stochastic model with a variability informed by the one in the historical record. The task-independent nature of AtmoRep enables skillful results for a diverse set of applications without specifically training for them and we demonstrate this for nowcasting, temporal interpolation, model correction, and counterfactuals. We also show that AtmoRep can be improved with additional data, for example radar observations, and that it can be extended to tasks such as downscaling. Our work establishes that large-scale neural networks can provide skillful, task-independent models of atmospheric dynamics. With this, they provide a novel means to make the large record of atmospheric observations accessible for applications and for scientific inquiry, complementing existing simulations based on first principles.

Warm-sector heavy rainfall often occurs along the coast of South China, and it is usually localized and long-lasting, making it challenging to predict. High-resolution numerical weather prediction (NWP) models are increasingly used to better resolve topographic features and forecast such high-impact weather events. However, when the grid spacing becomes comparable to the length scales of convection, known as the gray zone, the turbulent eddies in the atmospheric boundary layer are only partially resolved and parameterized to some extent. Whether using a convection parameterization (CP) scheme in the gray zone remains controversial. Scale-aware CP schemes are developed to enhance the representation of convective transport within the gray zone. The multi-scale Kain-Fritsch (MSKF) scheme includes modifications that allow for its effective implementation at a grid resolution as high as 2 km. In recent years, there has been an increasing application of machine learning (ML) models to various domains of atmospheric sciences, including the replacement of physical parameterizations with ML models. This work proposes a multi-output bidirectional long short-term memory (Bi-LSTM) model as a replace the scale-aware MSKF CP scheme. The Weather Research and Forecast (WRF) model is used to generate training and testing data over South China at a horizontal resolution of 5 km. Furthermore, the WRF model is coupled with the ML based CP scheme and compared with WRF simulations with original MSKF scheme. The results demonstrate that the Bi-LSTM model can achieve high accuracy, indicating the potential use of ML models to substitute the MSKF scheme in the gray zone.

Time series forecasting is widely used in extensive applications, such as traffic planning and weather forecasting. However, real-world time series usually present intricate temporal variations, making forecasting extremely challenging. Going beyond the mainstream paradigms of plain decomposition and multiperiodicity analysis, we analyze temporal variations in a novel view of multiscale-mixing, which is based on an intuitive but important observation that time series present distinct patterns in different sampling scales. The microscopic and the macroscopic information are reflected in fine and coarse scales respectively, and thereby complex variations can be inherently disentangled. Based on this observation, we propose TimeMixer as a fully MLP-based architecture with Past-Decomposable-Mixing (PDM) and Future-Multipredictor-Mixing (FMM) blocks to take full advantage of disentangled multiscale series in both past extraction and future prediction phases. Concretely, PDM applies the decomposition to multiscale series and further mixes the decomposed seasonal and trend components in fine-to-coarse and coarse-to-fine directions separately, which successively aggregates the microscopic seasonal and macroscopic trend information. FMM further ensembles multiple predictors to utilize complementary forecasting capabilities in multiscale observations. Consequently, TimeMixer is able to achieve consistent state-of-the-art performances in both long-term and short-term forecasting tasks with favorable run-time efficiency.

Neural operators have proven to be a promising approach for modeling spatiotemporal systems in the physical sciences. However, training these models for large systems can be quite challenging as they incur significant computational and memory expense -- these systems are often forced to rely on autoregressive time-stepping of the neural network to predict future temporal states. While this is effective in managing costs, it can lead to uncontrolled error growth over time and eventual instability. We analyze the sources of this autoregressive error growth using prototypical neural operator models for physical systems and explore ways to mitigate it. We introduce architectural and application-specific improvements that allow for careful control of instability-inducing operations within these models without inflating the compute/memory expense. We present results on several scientific systems that include Navier-Stokes fluid flow, rotating shallow water, and a high-resolution global weather forecasting system. We demonstrate that applying our design principles to neural operators leads to significantly lower errors for long-term forecasts as well as longer time horizons without qualitative signs of divergence compared to the original models for these systems. We open-source our https://github.com/mikemccabe210/stabilizing_neural_operators{code} for reproducibility.

We propose the Fourier Adaptive Lite Diffusion Architecture (FALDA), a novel probabilistic framework for time series forecasting. First, we introduce the Diffusion Model for Residual Regression (DMRR) framework, which unifies diffusion-based probabilistic regression methods. Within this framework, FALDA leverages Fourier-based decomposition to incorporate a component-specific architecture, enabling tailored modeling of individual temporal components. A conditional diffusion model is utilized to estimate the future noise term, while our proposed lightweight denoiser, DEMA (Decomposition MLP with AdaLN), conditions on the historical noise term to enhance denoising performance. Through mathematical analysis and empirical validation, we demonstrate that FALDA effectively reduces epistemic uncertainty, allowing probabilistic learning to primarily focus on aleatoric uncertainty. Experiments on six real-world benchmarks demonstrate that FALDA consistently outperforms existing probabilistic forecasting approaches across most datasets for long-term time series forecasting while achieving enhanced computational efficiency without compromising accuracy. Notably, FALDA also achieves superior overall performance compared to state-of-the-art (SOTA) point forecasting approaches, with improvements of up to 9%.

We address the problem of learning the dynamics of an unknown non-parametric system linking a target and a feature time series. The feature time series is measured on a sparse and irregular grid, while we have access to only a few points of the target time series. Once learned, we can use these dynamics to predict values of the target from the previous values of the feature time series. We frame this task as learning the solution map of a controlled differential equation (CDE). By leveraging the rich theory of signatures, we are able to cast this non-linear problem as a high-dimensional linear regression. We provide an oracle bound on the prediction error which exhibits explicit dependencies on the individual-specific sampling schemes. Our theoretical results are illustrated by simulations which show that our method outperforms existing algorithms for recovering the full time series while being computationally cheap. We conclude by demonstrating its potential on real-world epidemiological data.

We introduce Sundial, a family of native, flexible, and scalable time series foundation models. To predict the next-patch's distribution, we propose a TimeFlow Loss based on flow-matching, which facilitates native pre-training of Transformers on time series without discrete tokenization. Conditioned on arbitrary-length time series, our model is pre-trained without specifying any prior distribution and can generate multiple probable predictions, achieving flexibility in representation learning beyond using parametric densities. Towards time series foundation models, we leverage minimal but crucial adaptations of Transformers and curate TimeBench with 1 trillion time points, comprising mostly real-world datasets and synthetic data. By mitigating mode collapse through TimeFlow Loss, we pre-train a family of Sundial models on TimeBench, which exhibit unprecedented model capacity and generalization performance on zero-shot forecasting. In addition to presenting good scaling behavior, Sundial achieves new state-of-the-art on both point forecasting and probabilistic forecasting benchmarks. We believe that Sundial's pioneering generative paradigm will facilitate a wide variety of forecasting scenarios.

We consider the problem of forecasting motion from a single image, i.e., predicting how objects in the world are likely to move, without the ability to observe other parameters such as the object velocities or the forces applied to them. We formulate this task as conditional generation of dense trajectory grids with a model that closely follows the architecture of modern video generators but outputs motion trajectories instead of pixels. This approach captures scene-wide dynamics and uncertainty, yielding more accurate and diverse predictions than prior regressors and generators. We extensively evaluate our method on simulated data, demonstrate its effectiveness on downstream applications such as robotics, and show promising accuracy on real-world intuitive physics datasets. Although recent state-of-the-art video generators are often regarded as world models, we show that they struggle with forecasting motion from a single image, even in simple physical scenarios such as falling blocks or mechanical object interactions, despite fine-tuning on such data. We show that this limitation arises from the overhead of generating pixels rather than directly modeling motion.

Time series data is a prevalent form of data found in various fields. It consists of a series of measurements taken over time. Forecasting is a crucial application of time series models, where future values are predicted based on historical data. Accurate forecasting is essential for making well-informed decisions across industries. When it comes to electric vehicles (EVs), precise predictions play a key role in planning infrastructure development, load balancing, and energy management. This study introduces a BI-LSTM embedding denoising autoencoder model (BDM) designed to address time series problems, focusing on short-term EV charging load prediction. The performance of the proposed model is evaluated by comparing it with benchmark models like Transformer, CNN, RNN, LSTM, and GRU. Based on the results of the study, the proposed model outperforms the benchmark models in four of the five-time steps, demonstrating its effectiveness for time series forecasting. This research makes a significant contribution to enhancing time series forecasting, thereby improving decision-making processes.

Diffusion models have achieved state-of-the-art performance in generative modeling tasks across various domains. Prior works on time series diffusion models have primarily focused on developing conditional models tailored to specific forecasting or imputation tasks. In this work, we explore the potential of task-agnostic, unconditional diffusion models for several time series applications. We propose TSDiff, an unconditionally trained diffusion model for time series. Our proposed self-guidance mechanism enables conditioning TSDiff for downstream tasks during inference, without requiring auxiliary networks or altering the training procedure. We demonstrate the effectiveness of our method on three different time series tasks: forecasting, refinement, and synthetic data generation. First, we show that TSDiff is competitive with several task-specific conditional forecasting methods (predict). Second, we leverage the learned implicit probability density of TSDiff to iteratively refine the predictions of base forecasters with reduced computational overhead over reverse diffusion (refine). Notably, the generative performance of the model remains intact -- downstream forecasters trained on synthetic samples from TSDiff outperform forecasters that are trained on samples from other state-of-the-art generative time series models, occasionally even outperforming models trained on real data (synthesize).

Multivariate long-term and efficient time series forecasting is a key requirement for a variety of practical applications, and there are complex interleaving time dynamics in time series data that require decomposition modeling. Traditional time series decomposition methods are single and rely on fixed rules, which are insufficient for mining the potential information of the series and adapting to the dynamic characteristics of complex series. On the other hand, the Transformer-based models for time series forecasting struggle to effectively model long sequences and intricate dynamic relationships due to their high computational complexity. To overcome these limitations, we introduce KARMA, with an Adaptive Time Channel Decomposition module (ATCD) to dynamically extract trend and seasonal components. It further integrates a Hybrid Frequency-Time Decomposition module (HFTD) to further decompose Series into frequency-domain and time-domain. These components are coupled with multi-scale Mamba-based KarmaBlock to efficiently process global and local information in a coordinated manner. Experiments on eight real-world datasets from diverse domains well demonstrated that KARMA significantly outperforms mainstream baseline methods in both predictive accuracy and computational efficiency. Code and full results are available at this repository: https://github.com/yedadasd/KARMA

Recent years have witnessed remarkable advances in spatiotemporal predictive learning, with methods incorporating auxiliary inputs, complex neural architectures, and sophisticated training strategies. While SimVP has introduced a simpler, CNN-based baseline for this task, it still relies on heavy Unet-like architectures for spatial and temporal modeling, which still suffers from high complexity and computational overhead. In this paper, we propose SimVPv2, a streamlined model that eliminates the need for Unet architectures and demonstrates that plain stacks of convolutional layers, enhanced with an efficient Gated Spatiotemporal Attention mechanism, can deliver state-of-the-art performance. SimVPv2 not only simplifies the model architecture but also improves both performance and computational efficiency. On the standard Moving MNIST benchmark, SimVPv2 achieves superior performance compared to SimVP, with fewer FLOPs, about half the training time, and 60% faster inference efficiency. Extensive experiments across eight diverse datasets, including real-world tasks such as traffic forecasting and climate prediction, further demonstrate that SimVPv2 offers a powerful yet straightforward solution, achieving robust generalization across various spatiotemporal learning scenarios. We believe the proposed SimVPv2 can serve as a solid baseline to benefit the spatiotemporal predictive learning community.

We introduce a novel machine learning model for credit risk by combining tree-boosting with a latent spatio-temporal Gaussian process model accounting for frailty correlation. This allows for modeling non-linearities and interactions among predictor variables in a flexible data-driven manner and for accounting for spatio-temporal variation that is not explained by observable predictor variables. We also show how estimation and prediction can be done in a computationally efficient manner. In an application to a large U.S. mortgage credit risk data set, we find that both predictive default probabilities for individual loans and predictive loan portfolio loss distributions obtained with our novel approach are more accurate compared to conventional independent linear hazard models and also linear spatio-temporal models. Using interpretability tools for machine learning models, we find that the likely reasons for this outperformance are strong interaction and non-linear effects in the predictor variables and the presence of large spatio-temporal frailty effects.

Solving the optimal power flow (OPF) problem in real-time electricity market improves the efficiency and reliability in the integration of low-carbon energy resources into the power grids. To address the scalability and adaptivity issues of existing end-to-end OPF learning solutions, we propose a new graph neural network (GNN) framework for predicting the electricity market prices from solving OPFs. The proposed GNN-for-OPF framework innovatively exploits the locality property of prices and introduces physics-aware regularization, while attaining reduced model complexity and fast adaptivity to varying grid topology. Numerical tests have validated the learning efficiency and adaptivity improvements of our proposed method over existing approaches.

Time series modeling is a well-established problem, which often requires that methods (1) expressively represent complicated dependencies, (2) forecast long horizons, and (3) efficiently train over long sequences. State-space models (SSMs) are classical models for time series, and prior works combine SSMs with deep learning layers for efficient sequence modeling. However, we find fundamental limitations with these prior approaches, proving their SSM representations cannot express autoregressive time series processes. We thus introduce SpaceTime, a new state-space time series architecture that improves all three criteria. For expressivity, we propose a new SSM parameterization based on the companion matrix -- a canonical representation for discrete-time processes -- which enables SpaceTime's SSM layers to learn desirable autoregressive processes. For long horizon forecasting, we introduce a "closed-loop" variation of the companion SSM, which enables SpaceTime to predict many future time-steps by generating its own layer-wise inputs. For efficient training and inference, we introduce an algorithm that reduces the memory and compute of a forward pass with the companion matrix. With sequence length ell and state-space size d, we go from O(d ell) na\"ively to O(d + ell). In experiments, our contributions lead to state-of-the-art results on extensive and diverse benchmarks, with best or second-best AUROC on 6 / 7 ECG and speech time series classification, and best MSE on 14 / 16 Informer forecasting tasks. Furthermore, we find SpaceTime (1) fits AR(p) processes that prior deep SSMs fail on, (2) forecasts notably more accurately on longer horizons than prior state-of-the-art, and (3) speeds up training on real-world ETTh1 data by 73% and 80% relative wall-clock time over Transformers and LSTMs.

Ambient air pollution remains a critical issue in the United Kingdom, where data on air pollution concentrations form the foundation for interventions aimed at improving air quality. However, the current air pollution monitoring station network in the UK is characterized by spatial sparsity, heterogeneous placement, and frequent temporal data gaps, often due to issues such as power outages. We introduce a scalable data-driven supervised machine learning model framework designed to address temporal and spatial data gaps by filling missing measurements. This approach provides a comprehensive dataset for England throughout 2018 at a 1kmx1km hourly resolution. Leveraging machine learning techniques and real-world data from the sparsely distributed monitoring stations, we generate 355,827 synthetic monitoring stations across the study area, yielding data valued at approximately \pounds70 billion. Validation was conducted to assess the model's performance in forecasting, estimating missing locations, and capturing peak concentrations. The resulting dataset is of particular interest to a diverse range of stakeholders engaged in downstream assessments supported by outdoor air pollution concentration data for NO2, O3, PM10, PM2.5, and SO2. This resource empowers stakeholders to conduct studies at a higher resolution than was previously possible.

We introduce a new class of spatially stochastic physics and data informed deep latent models for parametric partial differential equations (PDEs) which operate through scalable variational neural processes. We achieve this by assigning probability measures to the spatial domain, which allows us to treat collocation grids probabilistically as random variables to be marginalised out. Adapting this spatial statistics view, we solve forward and inverse problems for parametric PDEs in a way that leads to the construction of Gaussian process models of solution fields. The implementation of these random grids poses a unique set of challenges for inverse physics informed deep learning frameworks and we propose a new architecture called Grid Invariant Convolutional Networks (GICNets) to overcome these challenges. We further show how to incorporate noisy data in a principled manner into our physics informed model to improve predictions for problems where data may be available but whose measurement location does not coincide with any fixed mesh or grid. The proposed method is tested on a nonlinear Poisson problem, Burgers equation, and Navier-Stokes equations, and we provide extensive numerical comparisons. We demonstrate significant computational advantages over current physics informed neural learning methods for parametric PDEs while improving the predictive capabilities and flexibility of these models.

Numerical simulation of non-linear partial differential equations plays a crucial role in modeling physical science and engineering phenomena, such as weather, climate, and aerodynamics. Recent Machine Learning (ML) models trained on low-resolution spatio-temporal signals have shown new promises in capturing important dynamics in high-resolution signals, under the condition that the models can effectively recover the missing details. However, this study shows that significant information is often lost in the low-resolution down-sampled features. To address such issues, we propose a new approach, namely Temporal Stencil Modeling (TSM), which combines the strengths of advanced time-series sequence modeling (with the HiPPO features) and state-of-the-art neural PDE solvers (with learnable stencil modeling). TSM aims to recover the lost information from the PDE trajectories and can be regarded as a temporal generalization of classic finite volume methods such as WENO. Our experimental results show that TSM achieves the new state-of-the-art simulation accuracy for 2-D incompressible Navier-Stokes turbulent flows: it significantly outperforms the previously reported best results by 19.9% in terms of the highly-correlated duration time and reduces the inference latency into 80%. We also show a strong generalization ability of the proposed method to various out-of-distribution turbulent flow settings. Our code is available at "https://github.com/Edward-Sun/TSM-PDE".

In trajectory forecasting tasks for traffic, future output trajectories can be computed by advancing the ego vehicle's state with predicted actions according to a kinematics model. By unrolling predicted trajectories via time integration and models of kinematic dynamics, predicted trajectories should not only be kinematically feasible but also relate uncertainty from one timestep to the next. While current works in probabilistic prediction do incorporate kinematic priors for mean trajectory prediction, variance is often left as a learnable parameter, despite uncertainty in one time step being inextricably tied to uncertainty in the previous time step. In this paper, we show simple and differentiable analytical approximations describing the relationship between variance at one timestep and that at the next with the kinematic bicycle model. These approximations can be easily incorporated with negligible additional overhead into any existing trajectory forecasting framework utilizing probabilistic predictions, whether it is autoregressive or one-shot prediction. In our results, we find that encoding the relationship between variance across timesteps works especially well in unoptimal settings, such as with small or noisy datasets. We observe up to a 50% performance boost in partial dataset settings and up to an 8% performance boost in large-scale learning compared to previous kinematic prediction methods on SOTA trajectory forecasting architectures out-of-the-box, with no fine-tuning. In this paper, we show four analytical formulations of probabilistic kinematic priors which can be used for any Gaussian Mixture Model (GMM)-based deep learning models, quantify the error bound on linear approximations applied during trajectory unrolling, and show results to evaluate each formulation in trajectory forecasting.

Traffic prediction is a typical spatio-temporal data mining task and has great significance to the public transportation system. Considering the demand for its grand application, we recognize key factors for an ideal spatio-temporal prediction method: efficient, lightweight, and effective. However, the current deep model-based spatio-temporal prediction solutions generally own intricate architectures with cumbersome optimization, which can hardly meet these expectations. To accomplish the above goals, we propose an intuitive and novel framework, MLPST, a pure multi-layer perceptron architecture for traffic prediction. Specifically, we first capture spatial relationships from both local and global receptive fields. Then, temporal dependencies in different intervals are comprehensively considered. Through compact and swift MLP processing, MLPST can well capture the spatial and temporal dependencies while requiring only linear computational complexity, as well as model parameters that are more than an order of magnitude lower than baselines. Extensive experiments validated the superior effectiveness and efficiency of MLPST against advanced baselines, and among models with optimal accuracy, MLPST achieves the best time and space efficiency.

Time-series forecasting is one of the most active research topics in artificial intelligence. Applications in real-world time series should consider two factors for achieving reliable predictions: modeling dynamic dependencies among multiple variables and adjusting the model's intrinsic hyperparameters. A still open gap in that literature is that statistical and ensemble learning approaches systematically present lower predictive performance than deep learning methods. They generally disregard the data sequence aspect entangled with multivariate data represented in more than one time series. Conversely, this work presents a novel neural network architecture for time-series forecasting that combines the power of graph evolution with deep recurrent learning on distinct data distributions; we named our method Recurrent Graph Evolution Neural Network (ReGENN). The idea is to infer multiple multivariate relationships between co-occurring time-series by assuming that the temporal data depends not only on inner variables and intra-temporal relationships (i.e., observations from itself) but also on outer variables and inter-temporal relationships (i.e., observations from other-selves). An extensive set of experiments was conducted comparing ReGENN with dozens of ensemble methods and classical statistical ones, showing sound improvement of up to 64.87% over the competing algorithms. Furthermore, we present an analysis of the intermediate weights arising from ReGENN, showing that by looking at inter and intra-temporal relationships simultaneously, time-series forecasting is majorly improved if paying attention to how multiple multivariate data synchronously evolve.

Machine learning (ML)-based weather models have rapidly risen to prominence due to their greater accuracy and speed than traditional forecasts based on numerical weather prediction (NWP), recently outperforming traditional ensembles in global probabilistic weather forecasting. This paper presents FGN, a simple, scalable and flexible modeling approach which significantly outperforms the current state-of-the-art models. FGN generates ensembles via learned model-perturbations with an ensemble of appropriately constrained models. It is trained directly to minimize the continuous rank probability score (CRPS) of per-location forecasts. It produces state-of-the-art ensemble forecasts as measured by a range of deterministic and probabilistic metrics, makes skillful ensemble tropical cyclone track predictions, and captures joint spatial structure despite being trained only on marginals.

Recent advancements in data-driven weather forecasting models have delivered deterministic models that outperform the leading operational forecast systems based on traditional, physics-based models. However, these data-driven models are typically trained with a mean squared error loss function, which causes smoothing of fine scales through a "double penalty" effect. We develop a simple, parameter-free modification to this loss function that avoids this problem by separating the loss attributable to decorrelation from the loss attributable to spectral amplitude errors. Fine-tuning the GraphCast model with this new loss function results in sharp deterministic weather forecasts, an increase of the model's effective resolution from 1,250km to 160km, improvements to ensemble spread, and improvements to predictions of tropical cyclone strength and surface wind extremes.

Extending the forecasting time is a critical demand for real applications, such as extreme weather early warning and long-term energy consumption planning. This paper studies the long-term forecasting problem of time series. Prior Transformer-based models adopt various self-attention mechanisms to discover the long-range dependencies. However, intricate temporal patterns of the long-term future prohibit the model from finding reliable dependencies. Also, Transformers have to adopt the sparse versions of point-wise self-attentions for long series efficiency, resulting in the information utilization bottleneck. Going beyond Transformers, we design Autoformer as a novel decomposition architecture with an Auto-Correlation mechanism. We break with the pre-processing convention of series decomposition and renovate it as a basic inner block of deep models. This design empowers Autoformer with progressive decomposition capacities for complex time series. Further, inspired by the stochastic process theory, we design the Auto-Correlation mechanism based on the series periodicity, which conducts the dependencies discovery and representation aggregation at the sub-series level. Auto-Correlation outperforms self-attention in both efficiency and accuracy. In long-term forecasting, Autoformer yields state-of-the-art accuracy, with a 38% relative improvement on six benchmarks, covering five practical applications: energy, traffic, economics, weather and disease. Code is available at this repository: https://github.com/thuml/Autoformer.

Current deep learning models for dynamics forecasting struggle with generalization. They can only forecast in a specific domain and fail when applied to systems with different parameters, external forces, or boundary conditions. We propose a model-based meta-learning method called DyAd which can generalize across heterogeneous domains by partitioning them into different tasks. DyAd has two parts: an encoder which infers the time-invariant hidden features of the task with weak supervision, and a forecaster which learns the shared dynamics of the entire domain. The encoder adapts and controls the forecaster during inference using adaptive instance normalization and adaptive padding. Theoretically, we prove that the generalization error of such procedure is related to the task relatedness in the source domain, as well as the domain differences between source and target. Experimentally, we demonstrate that our model outperforms state-of-the-art approaches on both turbulent flow and real-world ocean data forecasting tasks.

Motion forecasting is an essential task for autonomous driving, and utilizing information from infrastructure and other vehicles can enhance forecasting capabilities. Existing research mainly focuses on leveraging single-frame cooperative information to enhance the limited perception capability of the ego vehicle, while underutilizing the motion and interaction context of traffic participants observed from cooperative devices. In this paper, we propose a forecasting-oriented representation paradigm to utilize motion and interaction features from cooperative information. Specifically, we present V2X-Graph, a representative framework to achieve interpretable and end-to-end trajectory feature fusion for cooperative motion forecasting. V2X-Graph is evaluated on V2X-Seq in vehicle-to-infrastructure (V2I) scenarios. To further evaluate on vehicle-to-everything (V2X) scenario, we construct the first real-world V2X motion forecasting dataset V2X-Traj, which contains multiple autonomous vehicles and infrastructure in every scenario. Experimental results on both V2X-Seq and V2X-Traj show the advantage of our method. We hope both V2X-Graph and V2X-Traj will benefit the further development of cooperative motion forecasting. Find the project at https://github.com/AIR-THU/V2X-Graph.

Data-driven modeling based on machine learning (ML) is showing enormous potential for weather forecasting. Rapid progress has been made with impressive results for some applications. The uptake of ML methods could be a game-changer for the incremental progress in traditional numerical weather prediction (NWP) known as the 'quiet revolution' of weather forecasting. The computational cost of running a forecast with standard NWP systems greatly hinders the improvements that can be made from increasing model resolution and ensemble sizes. An emerging new generation of ML models, developed using high-quality reanalysis datasets like ERA5 for training, allow forecasts that require much lower computational costs and that are highly-competitive in terms of accuracy. Here, we compare for the first time ML-generated forecasts with standard NWP-based forecasts in an operational-like context, initialized from the same initial conditions. Focusing on deterministic forecasts, we apply common forecast verification tools to assess to what extent a data-driven forecast produced with one of the recently developed ML models (PanguWeather) matches the quality and attributes of a forecast from one of the leading global NWP systems (the ECMWF IFS). The results are very promising, with comparable skill for both global metrics and extreme events, when verified against both the operational analysis and synoptic observations. Increasing forecast smoothness and bias drift with forecast lead time are identified as current drawbacks of ML-based forecasts. A new NWP paradigm is emerging relying on inference from ML models and state-of-the-art analysis and reanalysis datasets for forecast initialization and model training.

The advent of universal time series forecasting models has revolutionized zero-shot forecasting across diverse domains, yet the critical role of data diversity in training these models remains underexplored. Existing large-scale time series datasets often suffer from inherent biases and imbalanced distributions, leading to suboptimal model performance and generalization. To address this gap, we introduce BLAST, a novel pre-training corpus designed to enhance data diversity through a balanced sampling strategy. First, BLAST incorporates 321 billion observations from publicly available datasets and employs a comprehensive suite of statistical metrics to characterize time series patterns. Then, to facilitate pattern-oriented sampling, the data is implicitly clustered using grid-based partitioning. Furthermore, by integrating grid sampling and grid mixup techniques, BLAST ensures a balanced and representative coverage of diverse patterns. Experimental results demonstrate that models pre-trained on BLAST achieve state-of-the-art performance with a fraction of the computational resources and training tokens required by existing methods. Our findings highlight the pivotal role of data diversity in improving both training efficiency and model performance for the universal forecasting task.

Energy time-series analysis describes the process of analyzing past energy observations and possibly external factors so as to predict the future. Different tasks are involved in the general field of energy time-series analysis and forecasting, with electric load demand forecasting, personalized energy consumption forecasting, as well as renewable energy generation forecasting being among the most common ones. Following the exceptional performance of Deep Learning (DL) in a broad area of vision tasks, DL models have successfully been utilized in time-series forecasting tasks. This paper aims to provide insight into various DL methods geared towards improving the performance in energy time-series forecasting tasks, with special emphasis in Greek Energy Market, and equip the reader with the necessary knowledge to apply these methods in practice.

Fourier Neural Operators (FNOs) have proven to be an efficient and effective method for resolution-independent operator learning in a broad variety of application areas across scientific machine learning. A key reason for their success is their ability to accurately model long-range dependencies in spatio-temporal data by learning global convolutions in a computationally efficient manner. To this end, FNOs rely on the discrete Fourier transform (DFT), however, DFTs cause visual and spectral artifacts as well as pronounced dissipation when learning operators in spherical coordinates since they incorrectly assume a flat geometry. To overcome this limitation, we generalize FNOs on the sphere, introducing Spherical FNOs (SFNOs) for learning operators on spherical geometries. We apply SFNOs to forecasting atmospheric dynamics, and demonstrate stable auto\-regressive rollouts for a year of simulated time (1,460 steps), while retaining physically plausible dynamics. The SFNO has important implications for machine learning-based simulation of climate dynamics that could eventually help accelerate our response to climate change.

Diffusion models offer a physically grounded framework for probabilistic weather forecasting, but their typical reliance on slow, iterative solvers during inference makes them impractical for subseasonal-to-seasonal (S2S) applications where long lead-times and domain-driven calibration are essential. To address this, we introduce Swift, a single-step consistency model that, for the first time, enables autoregressive finetuning of a probability flow model with a continuous ranked probability score (CRPS) objective. This eliminates the need for multi-model ensembling or parameter perturbations. Results show that Swift produces skillful 6-hourly forecasts that remain stable for up to 75 days, running 39times faster than state-of-the-art diffusion baselines while achieving forecast skill competitive with the numerical-based, operational IFS ENS. This marks a step toward efficient and reliable ensemble forecasting from medium-range to seasonal-scales.

California is a global leader in agricultural production, contributing 12.5% of the United States total output and ranking as the fifth-largest food and cotton supplier in the world. Despite the availability of extensive historical yield data from the USDA National Agricultural Statistics Service, accurate and timely crop yield forecasting remains a challenge due to the complex interplay of environmental, climatic, and soil-related factors. In this study, we introduce a comprehensive crop yield benchmark dataset covering over 70 crops across all California counties from 2008 to 2022. The benchmark integrates diverse data sources, including Landsat satellite imagery, daily climate records, monthly evapotranspiration, and high-resolution soil properties. To effectively learn from these heterogeneous inputs, we develop a multi-modal deep learning model tailored for county-level, crop-specific yield forecasting. The model employs stratified feature extraction and a timeseries encoder to capture spatial and temporal dynamics during the growing season. Static inputs such as soil characteristics and crop identity inform long-term variability. Our approach achieves an overall R2 score of 0.76 across all crops of unseen test dataset, highlighting strong predictive performance across California diverse agricultural regions. This benchmark and modeling framework offer a valuable foundation for advancing agricultural forecasting, climate adaptation, and precision farming. The full dataset and codebase are publicly available at our GitHub repository.

Implicit Neural Spatial Representation (INSR) has emerged as an effective representation of spatially-dependent vector fields. This work explores solving time-dependent PDEs with INSR. Classical PDE solvers introduce both temporal and spatial discretizations. Common spatial discretizations include meshes and meshless point clouds, where each degree-of-freedom corresponds to a location in space. While these explicit spatial correspondences are intuitive to model and understand, these representations are not necessarily optimal for accuracy, memory usage, or adaptivity. Keeping the classical temporal discretization unchanged (e.g., explicit/implicit Euler), we explore INSR as an alternative spatial discretization, where spatial information is implicitly stored in the neural network weights. The network weights then evolve over time via time integration. Our approach does not require any training data generated by existing solvers because our approach is the solver itself. We validate our approach on various PDEs with examples involving large elastic deformations, turbulent fluids, and multi-scale phenomena. While slower to compute than traditional representations, our approach exhibits higher accuracy and lower memory consumption. Whereas classical solvers can dynamically adapt their spatial representation only by resorting to complex remeshing algorithms, our INSR approach is intrinsically adaptive. By tapping into the rich literature of classic time integrators, e.g., operator-splitting schemes, our method enables challenging simulations in contact mechanics and turbulent flows where previous neural-physics approaches struggle. Videos and codes are available on the project page: http://www.cs.columbia.edu/cg/INSR-PDE/

Heliophysics is central to understanding and forecasting space weather events and solar activity. Despite decades of high-resolution observations from the Solar Dynamics Observatory (SDO), most models remain task-specific and constrained by scarce labeled data, limiting their capacity to generalize across solar phenomena. We introduce Surya, a 366M parameter foundation model for heliophysics designed to learn general-purpose solar representations from multi-instrument SDO observations, including eight Atmospheric Imaging Assembly (AIA) channels and five Helioseismic and Magnetic Imager (HMI) products. Surya employs a spatiotemporal transformer architecture with spectral gating and long--short range attention, pretrained on high-resolution solar image forecasting tasks and further optimized through autoregressive rollout tuning. Zero-shot evaluations demonstrate its ability to forecast solar dynamics and flare events, while downstream fine-tuning with parameter-efficient Low-Rank Adaptation (LoRA) shows strong performance on solar wind forecasting, active region segmentation, solar flare forecasting, and EUV spectra. Surya is the first foundation model in heliophysics that uses time advancement as a pretext task on full-resolution SDO data. Its novel architecture and performance suggest that the model is able to learn the underlying physics behind solar evolution.

Learning accurate predictive models of real-world dynamic phenomena (e.g., climate, biological) remains a challenging task. One key issue is that the data generated by both natural and artificial processes often comprise time series that are irregularly sampled and/or contain missing observations. In this work, we propose the Neural Continuous-Discrete State Space Model (NCDSSM) for continuous-time modeling of time series through discrete-time observations. NCDSSM employs auxiliary variables to disentangle recognition from dynamics, thus requiring amortized inference only for the auxiliary variables. Leveraging techniques from continuous-discrete filtering theory, we demonstrate how to perform accurate Bayesian inference for the dynamic states. We propose three flexible parameterizations of the latent dynamics and an efficient training objective that marginalizes the dynamic states during inference. Empirical results on multiple benchmark datasets across various domains show improved imputation and forecasting performance of NCDSSM over existing models.

Earth observation is a fundamental tool for monitoring the evolution of land use in specific areas of interest. Observing and precisely defining change, in this context, requires both time-series data and pixel-wise segmentations. To that end, we propose the DynamicEarthNet dataset that consists of daily, multi-spectral satellite observations of 75 selected areas of interest distributed over the globe with imagery from Planet Labs. These observations are paired with pixel-wise monthly semantic segmentation labels of 7 land use and land cover (LULC) classes. DynamicEarthNet is the first dataset that provides this unique combination of daily measurements and high-quality labels. In our experiments, we compare several established baselines that either utilize the daily observations as additional training data (semi-supervised learning) or multiple observations at once (spatio-temporal learning) as a point of reference for future research. Finally, we propose a new evaluation metric SCS that addresses the specific challenges associated with time-series semantic change segmentation. The data is available at: https://mediatum.ub.tum.de/1650201.

Truck parking on freight corridors faces the major challenge of insufficient parking spaces. This is exacerbated by the Hour-of-Service (HOS) regulations, which often result in unauthorized parking practices, causing safety concerns. It has been shown that providing accurate parking usage prediction can be a cost-effective solution to reduce unsafe parking practices. In light of this, existing studies have developed various methods to predict the usage of a truck parking site and have demonstrated satisfactory accuracy. However, these studies focused on a single parking site, and few approaches have been proposed to predict the usage of multiple truck parking sites considering spatio-temporal dependencies, due to the lack of data. This paper aims to fill this gap and presents the Regional Temporal Graph Convolutional Network (RegT-GCN) to predict parking usage across the entire state to provide more comprehensive truck parking information. The framework leverages the topological structures of truck parking site locations and historical parking data to predict the occupancy rate considering spatio-temporal dependencies across a state. To achieve this, we introduce a Regional Decomposition approach, which effectively captures the geographical characteristics of the truck parking locations and their spatial correlations. Evaluation results demonstrate that the proposed model outperforms other baseline models, showing the effectiveness of our regional decomposition. The code is available at https://github.com/raynbowy23/RegT-GCN.

Chaos and unpredictability are traditionally synonymous, yet large-scale machine learning methods recently have demonstrated a surprising ability to forecast chaotic systems well beyond typical predictability horizons. However, recent works disagree on whether specialized methods grounded in dynamical systems theory, such as reservoir computers or neural ordinary differential equations, outperform general-purpose large-scale learning methods such as transformers or recurrent neural networks. These prior studies perform comparisons on few individually-chosen chaotic systems, thereby precluding robust quantification of how statistical modeling choices and dynamical invariants of different chaotic systems jointly determine empirical predictability. Here, we perform the largest to-date comparative study of forecasting methods on the classical problem of forecasting chaos: we benchmark 24 state-of-the-art forecasting methods on a crowdsourced database of 135 low-dimensional systems with 17 forecast metrics. We find that large-scale, domain-agnostic forecasting methods consistently produce predictions that remain accurate up to two dozen Lyapunov times, thereby accessing a new long-horizon forecasting regime well beyond classical methods. We find that, in this regime, accuracy decorrelates with classical invariant measures of predictability like the Lyapunov exponent. However, in data-limited settings outside the long-horizon regime, we find that physics-based hybrid methods retain a comparative advantage due to their strong inductive biases.

In this paper, we present a novel trajectory prediction model for autonomous driving, combining a Characterized Diffusion Module and a Spatial-Temporal Interaction Network to address the challenges posed by dynamic and heterogeneous traffic environments. Our model enhances the accuracy and reliability of trajectory predictions by incorporating uncertainty estimation and complex agent interactions. Through extensive experimentation on public datasets such as NGSIM, HighD, and MoCAD, our model significantly outperforms existing state-of-the-art methods. We demonstrate its ability to capture the underlying spatial-temporal dynamics of traffic scenarios and improve prediction precision, especially in complex environments. The proposed model showcases strong potential for application in real-world autonomous driving systems.

The oceans are a source of an impressive mixture of complex data that could be used to uncover relationships yet to be discovered. Such data comes from the oceans and their surface, such as Automatic Identification System (AIS) messages used for tracking vessels' trajectories. AIS messages are transmitted over radio or satellite at ideally periodic time intervals but vary irregularly over time. As such, this paper aims to model the AIS message transmission behavior through neural networks for forecasting upcoming AIS messages' content from multiple vessels, particularly in a simultaneous approach despite messages' temporal irregularities as outliers. We present a set of experiments comprising multiple algorithms for forecasting tasks with horizon sizes of varying lengths. Deep learning models (e.g., neural networks) revealed themselves to adequately preserve vessels' spatial awareness regardless of temporal irregularity. We show how convolutional layers, feed-forward networks, and recurrent neural networks can improve such tasks by working together. Experimenting with short, medium, and large-sized sequences of messages, our model achieved 36/37/38% of the Relative Percentage Difference - the lower, the better, whereas we observed 92/45/96% on the Elman's RNN, 51/52/40% on the GRU, and 129/98/61% on the LSTM. These results support our model as a driver for improving the prediction of vessel routes when analyzing multiple vessels of diverging types simultaneously under temporally noise data.

A faster than real time forecast system for solar wind and interplanetary magnetic field transients that is driven by hourly updated solar magnetograms is proposed to provide a continuous nowcast of the solar corona (<0.1AU) and 24-hours forecast of the solar wind at 1 AU by solving a full 3-D MHD model. This new model has been inspired by the concept of relativity of simultaneity used in the theory of special relativity. It is based on time transformation between two coordinate systems: the solar rest frame and a boosted system in which the current observations of the solar magnetic field and tomorrow's measurement of the solar wind at 1 AU are simultaneous. In this paper we derive the modified governing equations for both hydrodynamics (HD) and magnetohydrodynamics (MHD) and present a new numerical algorithm that only modifies the conserved quantities but preserves the original HD/MHD numerical flux. The proposed method enables an efficient numerical implementation, and thus a significantly longer forecast time than the traditional method.

In remote control systems, transmitting large data volumes (e.g. video feeds) from wireless sensors to faraway controllers is challenging when the uplink channel capacity is limited (e.g. RedCap devices or massive wireless sensor networks). Furthermore, the controllers often only need the information-rich components of the original data. To address this, we propose a Time-Series Joint Embedding Predictive Architecture (TS-JEPA) and a semantic actor trained through self-supervised learning. This approach harnesses TS-JEPA's semantic representation power and predictive capabilities by capturing spatio-temporal correlations in the source data. We leverage this to optimize uplink channel utilization, while the semantic actor calculates control commands directly from the encoded representations, rather than from the original data. We test our model through multiple parallel instances of the well-known inverted cart-pole scenario, where the approach is validated through the maximization of stability under constrained uplink channel capacity.

Weather forecasting is a fundamental problem for anticipating and mitigating the impacts of climate change. Recently, data-driven approaches for weather forecasting based on deep learning have shown great promise, achieving accuracies that are competitive with operational systems. However, those methods often employ complex, customized architectures without sufficient ablation analysis, making it difficult to understand what truly contributes to their success. Here we introduce Stormer, a simple transformer model that achieves state-of-the-art performance on weather forecasting with minimal changes to the standard transformer backbone. We identify the key components of Stormer through careful empirical analyses, including weather-specific embedding, randomized dynamics forecast, and pressure-weighted loss. At the core of Stormer is a randomized forecasting objective that trains the model to forecast the weather dynamics over varying time intervals. During inference, this allows us to produce multiple forecasts for a target lead time and combine them to obtain better forecast accuracy. On WeatherBench 2, Stormer performs competitively at short to medium-range forecasts and outperforms current methods beyond 7 days, while requiring orders-of-magnitude less training data and compute. Additionally, we demonstrate Stormer's favorable scaling properties, showing consistent improvements in forecast accuracy with increases in model size and training tokens. Code and checkpoints are available at https://github.com/tung-nd/stormer.

Machine-learning-based parameterizations (i.e. representation of sub-grid processes) of global climate models or turbulent simulations have recently been proposed as a powerful alternative to physical, but empirical, representations, offering a lower computational cost and higher accuracy. Yet, those approaches still suffer from a lack of generalization and extrapolation beyond the training data, which is however critical to projecting climate change or unobserved regimes of turbulence. Here we show that a multi-fidelity approach, which integrates datasets of different accuracy and abundance, can provide the best of both worlds: the capacity to extrapolate leveraging the physically-based parameterization and a higher accuracy using the machine-learning-based parameterizations. In an application to climate modeling, the multi-fidelity framework yields more accurate climate projections without requiring major increase in computational resources. Our multi-fidelity randomized prior networks (MF-RPNs) combine physical parameterization data as low-fidelity and storm-resolving historical run's data as high-fidelity. To extrapolate beyond the training data, the MF-RPNs are tested on high-fidelity warming scenarios, +4K, data. We show the MF-RPN's capacity to return much more skillful predictions compared to either low- or high-fidelity (historical data) simulations trained only on one regime while providing trustworthy uncertainty quantification across a wide range of scenarios. Our approach paves the way for the use of machine-learning based methods that can optimally leverage historical observations or high-fidelity simulations and extrapolate to unseen regimes such as climate change.

There is a recent surge in the development of spatio-temporal forecasting models in the transportation domain. Long-range traffic forecasting, however, remains a challenging task due to the intricate and extensive spatio-temporal correlations observed in traffic networks. Current works primarily rely on road networks with graph structures and learn representations using graph neural networks (GNNs), but this approach suffers from over-smoothing problem in deep architectures. To tackle this problem, recent methods introduced the combination of GNNs with residual connections or neural ordinary differential equations (ODE). However, current graph ODE models face two key limitations in feature extraction: (1) they lean towards global temporal patterns, overlooking local patterns that are important for unexpected events; and (2) they lack dynamic semantic edges in their architectural design. In this paper, we propose a novel architecture called Graph-based Multi-ODE Neural Networks (GRAM-ODE) which is designed with multiple connective ODE-GNN modules to learn better representations by capturing different views of complex local and global dynamic spatio-temporal dependencies. We also add some techniques like shared weights and divergence constraints into the intermediate layers of distinct ODE-GNN modules to further improve their communication towards the forecasting task. Our extensive set of experiments conducted on six real-world datasets demonstrate the superior performance of GRAM-ODE compared with state-of-the-art baselines as well as the contribution of different components to the overall performance. The code is available at https://github.com/zbliu98/GRAM-ODE

Time series forecasting has been a widely explored task of great importance in many applications. However, it is common that real-world time series data are recorded in a short time period, which results in a big gap between the deep model and the limited and noisy time series. In this work, we propose to address the time series forecasting problem with generative modeling and propose a bidirectional variational auto-encoder (BVAE) equipped with diffusion, denoise, and disentanglement, namely D3VAE. Specifically, a coupled diffusion probabilistic model is proposed to augment the time series data without increasing the aleatoric uncertainty and implement a more tractable inference process with BVAE. To ensure the generated series move toward the true target, we further propose to adapt and integrate the multiscale denoising score matching into the diffusion process for time series forecasting. In addition, to enhance the interpretability and stability of the prediction, we treat the latent variable in a multivariate manner and disentangle them on top of minimizing total correlation. Extensive experiments on synthetic and real-world data show that D3VAE outperforms competitive algorithms with remarkable margins. Our implementation is available at https://github.com/PaddlePaddle/PaddleSpatial/tree/main/research/D3VAE.

Recent advancements in artificial intelligence (AI) for numerical weather prediction (NWP) have significantly transformed atmospheric modeling. AI NWP models outperform traditional physics-based systems, such as the Integrated Forecast System (IFS), across several global metrics while requiring fewer computational resources. However, existing AI NWP models face limitations related to training datasets and timestep choices, often resulting in artifacts that reduce model performance. To address these challenges, we introduce the Community Research Earth Digital Intelligence Twin (CREDIT) framework, developed at NSF NCAR. CREDIT provides a flexible, scalable, and user-friendly platform for training and deploying AI-based atmospheric models on high-performance computing systems. It offers an end-to-end pipeline for data preprocessing, model training, and evaluation, democratizing access to advanced AI NWP capabilities. We demonstrate CREDIT's potential through WXFormer, a novel deterministic vision transformer designed to predict atmospheric states autoregressively, addressing common AI NWP issues like compounding error growth with techniques such as spectral normalization, padding, and multi-step training. Additionally, to illustrate CREDIT's flexibility and state-of-the-art model comparisons, we train the FUXI architecture within this framework. Our findings show that both FUXI and WXFormer, trained on six-hourly ERA5 hybrid sigma-pressure levels, generally outperform IFS HRES in 10-day forecasts, offering potential improvements in efficiency and forecast accuracy. CREDIT's modular design enables researchers to explore various models, datasets, and training configurations, fostering innovation within the scientific community.

FourCastNet, short for Fourier Forecasting Neural Network, is a global data-driven weather forecasting model that provides accurate short to medium-range global predictions at 0.25^{circ} resolution. FourCastNet accurately forecasts high-resolution, fast-timescale variables such as the surface wind speed, precipitation, and atmospheric water vapor. It has important implications for planning wind energy resources, predicting extreme weather events such as tropical cyclones, extra-tropical cyclones, and atmospheric rivers. FourCastNet matches the forecasting accuracy of the ECMWF Integrated Forecasting System (IFS), a state-of-the-art Numerical Weather Prediction (NWP) model, at short lead times for large-scale variables, while outperforming IFS for variables with complex fine-scale structure, including precipitation. FourCastNet generates a week-long forecast in less than 2 seconds, orders of magnitude faster than IFS. The speed of FourCastNet enables the creation of rapid and inexpensive large-ensemble forecasts with thousands of ensemble-members for improving probabilistic forecasting. We discuss how data-driven deep learning models such as FourCastNet are a valuable addition to the meteorology toolkit to aid and augment NWP models.

Many businesses and industries nowadays rely on large quantities of time series data making time series forecasting an important research area. Global forecasting models that are trained across sets of time series have shown a huge potential in providing accurate forecasts compared with the traditional univariate forecasting models that work on isolated series. However, there are currently no comprehensive time series archives for forecasting that contain datasets of time series from similar sources available for the research community to evaluate the performance of new global forecasting algorithms over a wide variety of datasets. In this paper, we present such a comprehensive time series forecasting archive containing 20 publicly available time series datasets from varied domains, with different characteristics in terms of frequency, series lengths, and inclusion of missing values. We also characterise the datasets, and identify similarities and differences among them, by conducting a feature analysis. Furthermore, we present the performance of a set of standard baseline forecasting methods over all datasets across eight error metrics, for the benefit of researchers using the archive to benchmark their forecasting algorithms.

Accurate crop yield forecasting is essential for global food security. However, current AI models systematically underperform when yields deviate from historical trends. We attribute this to the lack of rich, physically grounded datasets directly linking atmospheric states to yields. To address this, we introduce VITA (Variational Inference Transformer for Asymmetric data), a variational pretraining framework that learns representations from large satellite-based weather datasets and transfers to the ground-based limited measurements available for yield prediction. VITA is trained using detailed meteorological variables as proxy targets during pretraining and learns to predict latent atmospheric states under a seasonality-aware sinusoidal prior. This allows the model to be fine-tuned using limited weather statistics during deployment. Applied to 763 counties in the U.S. Corn Belt, VITA achieves state-of-the-art performance in predicting corn and soybean yields across all evaluation scenarios, particularly during extreme years, with statistically significant improvements (paired t-test, p < 0.0001). Importantly, VITA outperforms prior frameworks like GNN-RNN without soil data, and bigger foundational models (e.g., Chronos-Bolt) with less compute, making it practical for real-world use--especially in data-scarce regions. This work highlights how domain-aware AI design can overcome data limitations and support resilient agricultural forecasting in a changing climate.

The performance of time series forecasting has recently been greatly improved by the introduction of transformers. In this paper, we propose a general multi-scale framework that can be applied to the state-of-the-art transformer-based time series forecasting models (FEDformer, Autoformer, etc.). By iteratively refining a forecasted time series at multiple scales with shared weights, introducing architecture adaptations, and a specially-designed normalization scheme, we are able to achieve significant performance improvements, from 5.5% to 38.5% across datasets and transformer architectures, with minimal additional computational overhead. Via detailed ablation studies, we demonstrate the effectiveness of each of our contributions across the architecture and methodology. Furthermore, our experiments on various public datasets demonstrate that the proposed improvements outperform their corresponding baseline counterparts. Our code is publicly available in https://github.com/BorealisAI/scaleformer.

Earth system models suffer from various structural and parametric errors in their representation of nonlinear, multi-scale processes, leading to uncertainties in their long-term projections. The effects of many of these errors (particularly those due to fast physics) can be quantified in short-term simulations, e.g., as differences between the predicted and observed states (analysis increments). With the increase in the availability of high-quality observations and simulations, learning nudging from these increments to correct model errors has become an active research area. However, most studies focus on using neural networks, which while powerful, are hard to interpret, are data-hungry, and poorly generalize out-of-distribution. Here, we show the capabilities of Model Error Discovery with Interpretability and Data Assimilation (MEDIDA), a general, data-efficient framework that uses sparsity-promoting equation-discovery techniques to learn model errors from analysis increments. Using two-layer quasi-geostrophic turbulence as the test case, MEDIDA is shown to successfully discover various linear and nonlinear structural/parametric errors when full observations are available. Discovery from spatially sparse observations is found to require highly accurate interpolation schemes. While NNs have shown success as interpolators in recent studies, here, they are found inadequate due to their inability to accurately represent small scales, a phenomenon known as spectral bias. We show that a general remedy, adding a random Fourier feature layer to the NN, resolves this issue enabling MEDIDA to successfully discover model errors from sparse observations. These promising results suggest that with further development, MEDIDA could be scaled up to models of the Earth system and real observations.

Artificial Intelligence (AI) weather prediction (AIWP) models are powerful tools for medium-range forecasts but often lack physical consistency, leading to outputs that violate conservation laws. This study introduces a set of novel physics-based schemes designed to enforce the conservation of global dry air mass, moisture budget, and total atmospheric energy in AIWP models. The schemes are highly modular, allowing for seamless integration into a wide range of AI model architectures. Forecast experiments are conducted to demonstrate the benefit of conservation schemes using FuXi, an example AIWP model, modified and adapted for 1.0-degree grid spacing. Verification results show that the conservation schemes can guide the model in producing forecasts that obey conservation laws. The forecast skills of upper-air and surface variables are also improved, with longer forecast lead times receiving larger benefits. Notably, large performance gains are found in the total precipitation forecasts, owing to the reduction of drizzle bias. The proposed conservation schemes establish a foundation for implementing other physics-based schemes in the future. They also provide a new way to integrate atmospheric domain knowledge into the design and refinement of AIWP models.

The body of research on classification of solar panel arrays from aerial imagery is increasing, yet there are still not many public benchmark datasets. This paper introduces two novel benchmark datasets for classifying and localizing solar panel arrays in Denmark: A human annotated dataset for classification and segmentation, as well as a classification dataset acquired using self-reported data from the Danish national building registry. We explore the performance of prior works on the new benchmark dataset, and present results after fine-tuning models using a similar approach as recent works. Furthermore, we train models of newer architectures and provide benchmark baselines to our datasets in several scenarios. We believe the release of these datasets may improve future research in both local and global geospatial domains for identifying and mapping of solar panel arrays from aerial imagery. The data is accessible at https://osf.io/aj539/.

Effective traffic prediction is a cornerstone of intelligent transportation systems, enabling precise forecasts of traffic flow, speed, and congestion. While traditional spatio-temporal graph neural networks (ST-GNNs) have achieved notable success in short-term traffic forecasting, their performance in long-term predictions remains limited. This challenge arises from over-squashing problem, where bottlenecks and limited receptive fields restrict information flow and hinder the modeling of global dependencies. To address these challenges, this study introduces a novel framework that incorporates virtual nodes, which are additional nodes added to the graph and connected to existing nodes, in order to aggregate information across the entire graph within a single GNN layer. Our proposed model incorporates virtual nodes by constructing a semi-adaptive adjacency matrix. This matrix integrates distance-based and adaptive adjacency matrices, allowing the model to leverage geographical information while also learning task-specific features from data. Experimental results demonstrate that the inclusion of virtual nodes significantly enhances long-term prediction accuracy while also improving layer-wise sensitivity to mitigate the over-squashing problem. Virtual nodes also offer enhanced explainability by focusing on key intersections and high-traffic areas, as shown by the visualization of their adjacency matrix weights on road network heat maps. Our advanced approach enhances the understanding and management of urban traffic systems, making it particularly well-suited for real-world applications.

Long-term forecasting of chaotic systems from short-term observations remains a fundamental and underexplored challenge due to the intrinsic sensitivity to initial conditions and the complex geometry of strange attractors. Existing approaches often rely on long-term training data or focus on short-term sequence correlations, struggling to maintain predictive stability and dynamical coherence over extended horizons. We propose PhyxMamba, a novel framework that integrates a Mamba-based state-space model with physics-informed principles to capture the underlying dynamics of chaotic systems. By reconstructing the attractor manifold from brief observations using time-delay embeddings, PhyxMamba extracts global dynamical features essential for accurate forecasting. Our generative training scheme enables Mamba to replicate the physical process, augmented by multi-token prediction and attractor geometry regularization for physical constraints, enhancing prediction accuracy and preserving key statistical invariants. Extensive evaluations on diverse simulated and real-world chaotic systems demonstrate that PhyxMamba delivers superior long-term forecasting and faithfully captures essential dynamical invariants from short-term data. This framework opens new avenues for reliably predicting chaotic systems under observation-scarce conditions, with broad implications across climate science, neuroscience, epidemiology, and beyond. Our code is open-source at https://github.com/tsinghua-fib-lab/PhyxMamba.

Pre-trained foundation models (FMs) have shown exceptional performance in univariate time series forecasting tasks. However, several practical challenges persist, including managing intricate dependencies among features and quantifying uncertainty in predictions. This study aims to tackle these critical limitations by introducing adapters; feature-space transformations that facilitate the effective use of pre-trained univariate time series FMs for multivariate tasks. Adapters operate by projecting multivariate inputs into a suitable latent space and applying the FM independently to each dimension. Inspired by the literature on representation learning and partially stochastic Bayesian neural networks, we present a range of adapters and optimization/inference strategies. Experiments conducted on both synthetic and real-world datasets confirm the efficacy of adapters, demonstrating substantial enhancements in forecasting accuracy and uncertainty quantification compared to baseline methods. Our framework, AdaPTS, positions adapters as a modular, scalable, and effective solution for leveraging time series FMs in multivariate contexts, thereby promoting their wider adoption in real-world applications. We release the code at https://github.com/abenechehab/AdaPTS.

The weather forecasting system is important for science and society, and significant achievements have been made in applying artificial intelligence (AI) to medium-range weather forecasting. However, existing AI-based weather forecasting models rely on analysis or reanalysis products from traditional numerical weather prediction (NWP) systems as initial conditions for making predictions. Initial states are typically generated by traditional data assimilation components, which are computational expensive and time-consuming. Here we present an AI-based data assimilation model, i.e., Adas, for global weather variables. By introducing the confidence matrix, Adas employs gated convolution to handle sparse observations and gated cross-attention for capturing the interactions between the background and observations. Further, we combine Adas with the advanced AI-based forecasting model (i.e., FengWu) to construct the first end-to-end AI-based global weather forecasting system: FengWu-Adas. We demonstrate that Adas can assimilate global observations to produce high-quality analysis, enabling the system operate stably for long term. Moreover, we are the first to apply the methods to real-world scenarios, which is more challenging and has considerable practical application potential. We have also achieved the forecasts based on the analyses generated by AI with a skillful forecast lead time exceeding that of the IFS for the first time.

While the popularity of physics-informed neural networks (PINNs) is steadily rising, to this date PINNs have not been successful in simulating dynamical systems whose solution exhibits multi-scale, chaotic or turbulent behavior. In this work we attribute this shortcoming to the inability of existing PINNs formulations to respect the spatio-temporal causal structure that is inherent to the evolution of physical systems. We argue that this is a fundamental limitation and a key source of error that can ultimately steer PINN models to converge towards erroneous solutions. We address this pathology by proposing a simple re-formulation of PINNs loss functions that can explicitly account for physical causality during model training. We demonstrate that this simple modification alone is enough to introduce significant accuracy improvements, as well as a practical quantitative mechanism for assessing the convergence of a PINNs model. We provide state-of-the-art numerical results across a series of benchmarks for which existing PINNs formulations fail, including the chaotic Lorenz system, the Kuramoto-Sivashinsky equation in the chaotic regime, and the Navier-Stokes equations in the turbulent regime. To the best of our knowledge, this is the first time that PINNs have been successful in simulating such systems, introducing new opportunities for their applicability to problems of industrial complexity.

Recent progress in neural forecasting accelerated improvements in the performance of large-scale forecasting systems. Yet, long-horizon forecasting remains a very difficult task. Two common challenges afflicting the task are the volatility of the predictions and their computational complexity. We introduce N-HiTS, a model which addresses both challenges by incorporating novel hierarchical interpolation and multi-rate data sampling techniques. These techniques enable the proposed method to assemble its predictions sequentially, emphasizing components with different frequencies and scales while decomposing the input signal and synthesizing the forecast. We prove that the hierarchical interpolation technique can efficiently approximate arbitrarily long horizons in the presence of smoothness. Additionally, we conduct extensive large-scale dataset experiments from the long-horizon forecasting literature, demonstrating the advantages of our method over the state-of-the-art methods, where N-HiTS provides an average accuracy improvement of almost 20% over the latest Transformer architectures while reducing the computation time by an order of magnitude (50 times). Our code is available at bit.ly/3VA5DoT

Time series are the primary data type used to record dynamic system measurements and generated in great volume by both physical sensors and online processes (virtual sensors). Time series analytics is therefore crucial to unlocking the wealth of information implicit in available data. With the recent advancements in graph neural networks (GNNs), there has been a surge in GNN-based approaches for time series analysis. These approaches can explicitly model inter-temporal and inter-variable relationships, which traditional and other deep neural network-based methods struggle to do. In this survey, we provide a comprehensive review of graph neural networks for time series analysis (GNN4TS), encompassing four fundamental dimensions: forecasting, classification, anomaly detection, and imputation. Our aim is to guide designers and practitioners to understand, build applications, and advance research of GNN4TS. At first, we provide a comprehensive task-oriented taxonomy of GNN4TS. Then, we present and discuss representative research works and introduce mainstream applications of GNN4TS. A comprehensive discussion of potential future research directions completes the survey. This survey, for the first time, brings together a vast array of knowledge on GNN-based time series research, highlighting foundations, practical applications, and opportunities of graph neural networks for time series analysis.

Global medium-range weather forecasting is critical to decision-making across many social and economic domains. Traditional numerical weather prediction uses increased compute resources to improve forecast accuracy, but cannot directly use historical weather data to improve the underlying model. We introduce a machine learning-based method called "GraphCast", which can be trained directly from reanalysis data. It predicts hundreds of weather variables, over 10 days at 0.25 degree resolution globally, in under one minute. We show that GraphCast significantly outperforms the most accurate operational deterministic systems on 90% of 1380 verification targets, and its forecasts support better severe event prediction, including tropical cyclones, atmospheric rivers, and extreme temperatures. GraphCast is a key advance in accurate and efficient weather forecasting, and helps realize the promise of machine learning for modeling complex dynamical systems.

In the face of escalating climate changes, typhoon intensities and their ensuing damage have surged. Accurate trajectory prediction is crucial for effective damage control. Traditional physics-based models, while comprehensive, are computationally intensive and rely heavily on the expertise of forecasters. Contemporary data-driven methods often rely on reanalysis data, which can be considered to be the closest to the true representation of weather conditions. However, reanalysis data is not produced in real-time and requires time for adjustment because prediction models are calibrated with observational data. This reanalysis data, such as ERA5, falls short in challenging real-world situations. Optimal preparedness necessitates predictions at least 72 hours in advance, beyond the capabilities of standard physics models. In response to these constraints, we present an approach that harnesses real-time Unified Model (UM) data, sidestepping the limitations of reanalysis data. Our model provides predictions at 6-hour intervals for up to 72 hours in advance and outperforms both state-of-the-art data-driven methods and numerical weather prediction models. In line with our efforts to mitigate adversities inflicted by typhoons, we release our preprocessed PHYSICS TRACK dataset, which includes ERA5 reanalysis data, typhoon best-track, and UM forecast data.

A key aspect of temporal domains is the ability to make predictions multiple time steps into the future, a process known as multi-step forecasting (MSF). At the core of this process is selecting a forecasting strategy, however, with no existing frameworks to map out the space of strategies, practitioners are left with ad-hoc methods for strategy selection. In this work, we propose Stratify, a parameterised framework that addresses multi-step forecasting, unifying existing strategies and introducing novel, improved strategies. We evaluate Stratify on 18 benchmark datasets, five function classes, and short to long forecast horizons (10, 20, 40, 80). In over 84% of 1080 experiments, novel strategies in Stratify improved performance compared to all existing ones. Importantly, we find that no single strategy consistently outperforms others in all task settings, highlighting the need for practitioners explore the Stratify space to carefully search and select forecasting strategies based on task-specific requirements. Our results are the most comprehensive benchmarking of known and novel forecasting strategies. We make code available to reproduce our results.

We present Timer-XL, a generative Transformer for unified time series forecasting. To uniformly predict 1D and 2D time series, we generalize next token prediction, predominantly adopted for causal generation of 1D sequences, to multivariate next token prediction. The proposed paradigm uniformly formulates various forecasting scenarios as a long-context generation problem. We opt for the generative Transformer, which can capture global-range and causal dependencies while providing contextual flexibility, to implement unified forecasting on univariate series characterized by non-stationarity, multivariate time series with complicated dynamics and correlations, and covariate-informed contexts that include both endogenous and exogenous variables. Technically, we propose a universal TimeAttention to facilitate generative Transformers on time series, which can effectively capture fine-grained intra- and inter-series dependencies of flattened time series tokens (patches) and is further strengthened by position embeddings in both temporal and variable dimensions. Timer-XL achieves state-of-the-art performance across challenging forecasting benchmarks through a unified approach. As a large time series model, it demonstrates notable model transferability by large-scale pre-training, as well as contextual flexibility in token lengths, positioning it as a one-for-all forecaster.

In this paper, we present a new approach to time series forecasting. Time series data are prevalent in many scientific and engineering disciplines. Time series forecasting is a crucial task in modeling time series data, and is an important area of machine learning. In this work we developed a novel method that employs Transformer-based machine learning models to forecast time series data. This approach works by leveraging self-attention mechanisms to learn complex patterns and dynamics from time series data. Moreover, it is a generic framework and can be applied to univariate and multivariate time series data, as well as time series embeddings. Using influenza-like illness (ILI) forecasting as a case study, we show that the forecasting results produced by our approach are favorably comparable to the state-of-the-art.