Diffusion models are a powerful tool for probabilistic forecasting, yet most applications in high-dimensional chaotic systems predict future snapshots one-by-one. This common approach struggles to model complex temporal dependencies and fails to explicitly account for the progressive growth of uncertainty inherent to such systems. While rolling diffusion frameworks, which apply increasing noise to forecasts at longer lead times, have been proposed to address this, their integration with state-of-the-art, high-fidelity diffusion techniques remains a significant challenge. We tackle this problem by introducing Elucidated Rolling Diffusion Models (ERDM), the first framework to successfully unify a rolling forecast structure with the principled, performant design of Elucidated Diffusion Models (EDM). To do this, we adapt the core EDM components-its noise schedule, network preconditioning, and Heun sampler-to the rolling forecast setting. The success of this integration is driven by three key contributions: (i) a novel loss weighting scheme that focuses model capacity on the mid-range forecast horizons where determinism gives way to stochasticity; (ii) an efficient initialization strategy using a pre-trained EDM for the initial window; and (iii) a bespoke hybrid sequence architecture for robust spatiotemporal feature extraction under progressive denoising. On 2D Navier-Stokes simulations and ERA5 global weather forecasting at 1.5^\circ resolution, ERDM consistently outperforms key diffusion-based baselines, including conditional autoregressive EDM. ERDM offers a flexible and powerful general framework for tackling diffusion-based sequence generation problems where modeling escalating uncertainty is paramount. Code is available at: https://github.com/salvaRC/erdm
The advent of Large Weather Models (LWMs) has marked a turning point in data-driven forecasting, with many models now outperforming traditional numerical systems in the medium range. However, achieving stable, long-range autoregressive forecasts beyond a few weeks remains a significant challenge. Prevailing state-of-the-art models that achieve year-long stability, such as SFNO and DLWP-HPX, have relied on transforming input data onto non-standard spatial domains like spherical harmonics or HEALPix meshes. This has led to the prevailing assumption that such representations are necessary to enforce physical consistency and long-term stability. This paper challenges that assumption by investigating whether comparable long-range performance can be achieved on the standard latitude-longitude grid. We introduce AtmosMJ, a deep convolutional network that operates directly on ERA5 data without any spherical remapping. The model's stability is enabled by a novel Gated Residual Fusion (GRF) mechanism, which adaptively moderates feature updates to prevent error accumulation over long recursive simulations. Our results demonstrate that AtmosMJ produces stable and physically plausible forecasts for about 500 days. In quantitative evaluations, it achieves competitive 10-day forecast accuracy against models like Pangu-Weather and GraphCast, all while requiring a remarkably low training budget of 5.7 days on a V100 GPU. Our findings suggest that efficient architectural design, rather than non-standard data representation, can be the key to unlocking stable and computationally efficient long-range weather prediction.
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 crucial for managing risks and economic planning, particularly in tropical Africa, where extreme events severely impact livelihoods. Yet, existing forecasting methods often struggle with the region's complex, non-linear weather patterns. This study benchmarks deep recurrent neural networks such as $\texttt{LSTM, GRU, BiLSTM, BiGRU}$, and Kolmogorov-Arnold-based models $(\texttt{KAN} and \texttt{TKAN})$ for daily forecasting of temperature, precipitation, and pressure in two tropical cities: Abidjan, Cote d'Ivoire (Ivory Coast) and Kigali (Rwanda). We further introduce two customized variants of $ \texttt{TKAN}$ that replace its original $\texttt{SiLU}$ activation function with $ \texttt{GeLU}$ and \texttt{MiSH}, respectively. Using station-level meteorological data spanning from 2010 to 2024, we evaluate all the models on standard regression metrics. $\texttt{KAN}$ achieves temperature prediction ($R^2=0.9986$ in Abidjan, $0.9998$ in Kigali, $\texttt{MSE} < 0.0014~^\circ C ^2$), while $\texttt{TKAN}$ variants minimize absolute errors for precipitation forecasting in low-rainfall regimes. The customized $\texttt{TKAN}$ models demonstrate improvements over the standard $\texttt{TKAN}$ across both datasets. Classical \texttt{RNNs} remain highly competitive for atmospheric pressure ($R^2 \approx 0.83{-}0.86$), outperforming $\texttt{KAN}$-based models in this task. These results highlight the potential of spline-based neural architectures for efficient and data-efficient forecasting.
Weather forecasting is essential but remains computationally intensive and physically incomplete in traditional numerical weather prediction (NWP) methods. Deep learning (DL) models offer efficiency and accuracy but often ignore physical laws, limiting interpretability and generalization. We propose PhyDL-NWP, a physics-guided deep learning framework that integrates physical equations with latent force parameterization into data-driven models. It predicts weather variables from arbitrary spatiotemporal coordinates, computes physical terms via automatic differentiation, and uses a physics-informed loss to align predictions with governing dynamics. PhyDL-NWP enables resolution-free downscaling by modeling weather as a continuous function and fine-tunes pre-trained models with minimal overhead, achieving up to 170x faster inference with only 55K parameters. Experiments show that PhyDL-NWP improves both forecasting performance and physical consistency.
Accelerating the solution of nonlinear partial differential equations (PDEs) while maintaining accuracy at coarse spatiotemporal resolution remains a key challenge in scientific computing. Physics-informed machine learning (ML) methods such as Physics-Informed Neural Networks (PINNs) introduce prior knowledge through loss functions to ensure physical consistency, but their "soft constraints" are usually not strictly satisfied. Here, we propose LaPON, an operator network inspired by the Lagrange's mean value theorem, which embeds prior knowledge directly into the neural network architecture instead of the loss function, making the neural network naturally satisfy the given constraints. This is a hybrid framework that combines neural operators with traditional numerical methods, where neural operators are used to compensate for the effect of discretization errors on the analytical scale in under-resolution simulations. As evaluated on turbulence problem modeled by the Navier-Stokes equations (NSE), the multiple time step extrapolation accuracy and stability of LaPON exceed the direct numerical simulation baseline at 8x coarser grids and 8x larger time steps, while achieving a vorticity correlation of more than 0.98 with the ground truth. It is worth noting that the model can be well generalized to unseen flow states, such as turbulence with different forcing, without retraining. In addition, with the same training data, LaPON's comprehensive metrics on the out-of-distribution test set are at least approximately twice as good as two popular ML baseline methods. By combining numerical computing with machine learning, LaPON provides a scalable and reliable solution for high-fidelity fluid dynamics simulation, showing the potential for wide application in fields such as weather forecasting and engineering design.
Time series forecasting has important applications in financial analysis, weather forecasting, and traffic management. However, existing deep learning models are limited in processing non-stationary time series data because they cannot effectively capture the statistical characteristics that change over time. To address this problem, this paper proposes a new framework, AEFIN, which enhances the information sharing ability between stable and unstable components by introducing a cross-attention mechanism, and combines Fourier analysis networks with MLP to deeply explore the seasonal patterns and trend characteristics in unstable components. In addition, we design a new loss function that combines time-domain stability constraints, time-domain instability constraints, and frequency-domain stability constraints to improve the accuracy and robustness of forecasting. Experimental results show that AEFIN outperforms the most common models in terms of mean square error and mean absolute error, especially under non-stationary data conditions, and shows excellent forecasting capabilities. This paper provides an innovative solution for the modeling and forecasting of non-stationary time series data, and contributes to the research of deep learning for complex time series.
AI-based systems, such as Google's GenCast, have recently redefined the state of the art in weather forecasting, offering more accurate and timely predictions of both everyday weather and extreme events. While these systems are on the verge of replacing traditional meteorological methods, they also introduce new vulnerabilities into the forecasting process. In this paper, we investigate this threat and present a novel attack on autoregressive diffusion models, such as those used in GenCast, capable of manipulating weather forecasts and fabricating extreme events, including hurricanes, heat waves, and intense rainfall. The attack introduces subtle perturbations into weather observations that are statistically indistinguishable from natural noise and change less than 0.1% of the measurements - comparable to tampering with data from a single meteorological satellite. As modern forecasting integrates data from nearly a hundred satellites and many other sources operated by different countries, our findings highlight a critical security risk with the potential to cause large-scale disruptions and undermine public trust in weather prediction.
Solar flares are among the most powerful and dynamic events in the solar system, resulting from the sudden release of magnetic energy stored in the Sun's atmosphere. These energetic bursts of electromagnetic radiation can release up to 10^32 erg of energy, impacting space weather and posing risks to technological infrastructure and therefore require accurate forecasting of solar flare occurrences and intensities. This study evaluates the predictive performance of three machine learning algorithms: Random Forest, k-Nearest Neighbors (KNN), and Extreme Gradient Boosting (XGBoost) for classifying solar flares into 4 categories (B, C, M, X). Using the dataset of 13 SHARP parameters, the effectiveness of the models was evaluated in binary and multiclass classification tasks. The analysis utilized 8 principal components (PC), capturing 95% of data variance, and 100 PCs, capturing 97.5% of variance. Our approach uniquely combines binary and multiclass classification with different levels of dimensionality reduction, an innovative methodology not previously explored in the context of solar flare prediction. Employing a 10-fold stratified cross-validation and grid search for hyperparameter tuning ensured robust model evaluation. Our findings indicate that Random Forest and XGBoost consistently demonstrate strong performance across all metrics, benefiting significantly from increased dimensionality. The insights of this study enhance future research by optimizing dimensionality reduction techniques and informing model selection for astrophysical tasks. By integrating this newly acquired knowledge into future research, more accurate space weather forecasting systems can be developed, along with a deeper understanding of solar physics.
In machine learning forecasting, standard error metrics such as mean absolute error (MAE) and mean squared error (MSE) quantify discrepancies between predictions and target values. However, these metrics do not directly evaluate the physical and/or dynamical consistency of forecasts, an increasingly critical concern in scientific and engineering applications. Indeed, a fundamental yet often overlooked question is whether machine learning forecasts preserve the dynamical behavior of the underlying system. Addressing this issue is essential for assessing the fidelity of machine learning models and identifying potential failure modes, particularly in applications where maintaining correct dynamical behavior is crucial. In this work, we investigate the relationship between standard forecasting error metrics, such as MAE and MSE, and the dynamical properties of the underlying system. To achieve this goal, we use two recently developed dynamical indices: the instantaneous dimension ($d$), and the inverse persistence ($\theta$). Our results indicate that larger forecast errors -- e.g., higher MSE -- tend to occur in states with higher $d$ (higher complexity) and higher $\theta$ (lower persistence). To further assess dynamical consistency, we propose error metrics based on the dynamical indices that measure the discrepancy of the forecasted $d$ and $\theta$ versus their correct values. Leveraging these dynamical indices-based metrics, we analyze direct and recursive forecasting strategies for three canonical datasets -- Lorenz, Kuramoto-Sivashinsky equation, and Kolmogorov flow -- as well as a real-world weather forecasting task. Our findings reveal substantial distortions in dynamical properties in ML forecasts, especially for long forecast lead times or long recursive simulations, providing complementary information on ML forecast fidelity that can be used to improve ML models.
Machine learning is revolutionizing global weather forecasting, with models that efficiently produce highly accurate forecasts. Apart from global forecasting there is also a large value in high-resolution regional weather forecasts, focusing on accurate simulations of the atmosphere for a limited area. Initial attempts have been made to use machine learning for such limited area scenarios, but these experiments do not consider realistic forecasting settings and do not investigate the many design choices involved. We present a framework for building kilometer-scale machine learning limited area models with boundary conditions imposed through a flexible boundary forcing method. This enables boundary conditions defined either from reanalysis or operational forecast data. Our approach employs specialized graph constructions with rectangular and triangular meshes, along with multi-step rollout training strategies to improve temporal consistency. We perform systematic evaluation of different design choices, including the boundary width, graph construction and boundary forcing integration. Models are evaluated across both a Danish and a Swiss domain, two regions that exhibit different orographical characteristics. Verification is performed against both gridded analysis data and in-situ observations, including a case study for the storm Ciara in February 2020. Both models achieve skillful predictions across a wide range of variables, with our Swiss model outperforming the numerical weather prediction baseline for key surface variables. With their substantially lower computational cost, our findings demonstrate great potential for machine learning limited area models in the future of regional weather forecasting.
Climate science studies the structure and dynamics of Earth's climate system and seeks to understand how climate changes over time, where the data is usually stored in the format of time series, recording the climate features, geolocation, time attributes, etc. Recently, much research attention has been paid to the climate benchmarks. In addition to the most common task of weather forecasting, several pioneering benchmark works are proposed for extending the modality, such as domain-specific applications like tropical cyclone intensity prediction and flash flood damage estimation, or climate statement and confidence level in the format of natural language. To further motivate the artificial general intelligence development for climate science, in this paper, we first contribute a multi-modal climate benchmark, i.e., ClimateBench-M, which aligns (1) the time series climate data from ERA5, (2) extreme weather events data from NOAA, and (3) satellite image data from NASA HLS based on a unified spatial-temporal granularity. Second, under each data modality, we also propose a simple but strong generative method that could produce competitive performance in weather forecasting, thunderstorm alerts, and crop segmentation tasks in the proposed ClimateBench-M. The data and code of ClimateBench-M are publicly available at https://github.com/iDEA-iSAIL-Lab-UIUC/ClimateBench-M.
Graphical forecasting models learn the structure of time series data via projecting onto a graph, with recent techniques capturing spatial-temporal associations between variables via edge weights. Hierarchical variants offer a distinct advantage by analysing the time series across multiple resolutions, making them particularly effective in tasks like global weather forecasting, where low-resolution variable interactions are significant. A critical challenge in hierarchical models is information loss during forward or backward passes through the hierarchy. We propose the Hierarchical Graph Flow (HiGFlow) network, which introduces a memory buffer variable of dynamic size to store previously seen information across variable resolutions. We theoretically show two key results: HiGFlow reduces smoothness when mapping onto new feature spaces in the hierarchy and non-strictly enhances the utility of message-passing by improving Weisfeiler-Lehman (WL) expressivity. Empirical results demonstrate that HiGFlow outperforms state-of-the-art baselines, including transformer models, by at least an average of 6.1% in MAE and 6.2% in RMSE. Code is available at https://github.com/TB862/ HiGFlow.git.
We present WeatherMesh-3 (WM-3), an operational transformer-based global weather forecasting system that improves the state of the art in both accuracy and computational efficiency. We introduce the following advances: 1) a latent rollout that enables arbitrary-length predictions in latent space without intermediate encoding or decoding; and 2) a modular architecture that flexibly utilizes mixed-horizon processors and encodes multiple real-time analyses to create blended initial conditions. WM-3 generates 14-day global forecasts at 0.25-degree resolution in 12 seconds on a single RTX 4090. This represents a >100,000-fold speedup over traditional NWP approaches while achieving superior accuracy with up to 37.7% improvement in RMSE over operational models, requiring only a single consumer-grade GPU for deployment. We aim for WM-3 to democratize weather forecasting by providing an accessible, lightweight model for operational use while pushing the performance boundaries of machine learning-based weather prediction.
Modern fire management systems increasingly rely on satellite data and weather forecasting; however, access to comprehensive datasets remains limited due to proprietary restrictions. Despite the ecological significance of wildfires, large-scale, multi-regional research is constrained by data scarcity. Russian diverse ecosystems play a crucial role in shaping Eurasian fire dynamics, yet they remain underexplored. This study addresses existing gaps by introducing an open-access dataset that captures detailed fire incidents alongside corresponding meteorological conditions. We present one of the most extensive datasets available for wildfire analysis in Russia, covering 13 consecutive months of observations. Leveraging machine learning techniques, we conduct exploratory data analysis and develop predictive models to identify key fire behavior patterns across different fire categories and ecosystems. Our results highlight the critical influence of environmental factor patterns on fire occurrence and spread behavior. By improving the understanding of wildfire dynamics in Eurasia, this work contributes to more effective, data-driven approaches for proactive fire management in the face of evolving environmental conditions.
Neural operators aim to approximate the solution operator of a system of differential equations purely from data. They have shown immense success in modeling complex dynamical systems across various domains. However, the occurrence of uncertainties inherent in both model and data has so far rarely been taken into account\textemdash{}a critical limitation in complex, chaotic systems such as weather forecasting. In this paper, we introduce the probabilistic neural operator (PNO), a framework for learning probability distributions over the output function space of neural operators. PNO extends neural operators with generative modeling based on strictly proper scoring rules, integrating uncertainty information directly into the training process. We provide a theoretical justification for the approach and demonstrate improved performance in quantifying uncertainty across different domains and with respect to different baselines. Furthermore, PNO requires minimal adjustment to existing architectures, shows improved performance for most probabilistic prediction tasks, and leads to well-calibrated predictive distributions and adequate uncertainty representations even for long dynamical trajectories. Implementing our approach into large-scale models for physical applications can lead to improvements in corresponding uncertainty quantification and extreme event identification, ultimately leading to a deeper understanding of the prediction of such surrogate models.
State-space formulations allow for Gaussian process (GP) regression with linear-in-time computational cost in spatio-temporal settings, but performance typically suffers in the presence of outliers. In this paper, we adapt and specialise the robust and conjugate GP (RCGP) framework of Altamirano et al. (2024) to the spatio-temporal setting. In doing so, we obtain an outlier-robust spatio-temporal GP with a computational cost comparable to classical spatio-temporal GPs. We also overcome the three main drawbacks of RCGPs: their unreliable performance when the prior mean is chosen poorly, their lack of reliable uncertainty quantification, and the need to carefully select a hyperparameter by hand. We study our method extensively in finance and weather forecasting applications, demonstrating that it provides a reliable approach to spatio-temporal modelling in the presence of outliers.
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.
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.
Data assimilation plays a pivotal role in understanding and predicting turbulent systems within geoscience and weather forecasting, where data assimilation is used to address three fundamental challenges, i.e., high-dimensionality, nonlinearity, and partial observations. Recent advances in machine learning (ML)-based data assimilation methods have demonstrated encouraging results. In this work, we develop an ensemble score filter (EnSF) that integrates image inpainting to solve the data assimilation problems with partial observations. The EnSF method exploits an exclusively designed training-free diffusion models to solve high-dimensional nonlinear data assimilation problems. Its performance has been successfully demonstrated in the context of having full observations, i.e., all the state variables are directly or indirectly observed. However, because the EnSF does not use a covariance matrix to capture the dependence between the observed and unobserved state variables, it is nontrivial to extend the original EnSF method to the partial observation scenario. In this work, we incorporate various image inpainting techniques into the EnSF to predict the unobserved states during data assimilation. At each filtering step, we first use the diffusion model to estimate the observed states by integrating the likelihood information into the score function. Then, we use image inpainting methods to predict the unobserved state variables. We demonstrate the performance of the EnSF with inpainting by tracking the Surface Quasi-Geostrophic (SQG) model dynamics under a variety of scenarios. The successful proof of concept paves the way to more in-depth investigations on exploiting modern image inpainting techniques to advance data assimilation methodology for practical geoscience and weather forecasting problems.