PINA-Net: Physics-Constrained Nonautoregressive Network for Spatiotemporal Meteorological Forecasting in Complex Maritime Environments

Spherical Physics-informed Neural Operator with Multi-scale Coupling for Meteorological Downscaling

Climate Physics Dynamic Matching

Deep generative models such as flow matching and diffusion models have shown potential for learning complex dynamical systems, but typically act as black boxes that neglect underlying physical structure, while physics-based models governed by partial differential equations are often incomplete due to missing source terms, or uncertain parametrisations. We present Climate Physics Dynamic Matching (ClimPhyDM), a variational simulation-free dynamics informed framework for weather forecasting that combines an advection-type physics prior with data-driven components in a variational framework. % to capture the stochasticity and multi-modality of unresolved atmospheric dynamics. On the ERA5 benchmark at hourly (42-hour) and monthly (5-month) resolutions, ClimPhyDM outperforms ClimODE, and GB-DM, keeping the lower error at extended horizon, indicating improved temporal stability and resistance to error accumulation, while its simulation-free paradigm also enables training on a single modest 12 GB consumer GPU.

DPCD-Net: Data-Physics Co-Driven Network for Tropical Cyclone Trajectory and Intensity Prediction

Tropical cyclones (TCs) are among the most destructive weather systems in the geophysical environment. Accurate and efficient prediction of tropical cyclone trajectories and intensities is critical for disaster mitigation, including the prevention of property damage and reduction of casualties. While deep learning has advanced TC prediction, existing models still struggle to represent the coupled dynamics among environmental fields and the internal variability of key meteorological factors. In this study, we propose a Data-Physics Co-Driven Network (DPCD-Net) based on a generative adversarial framework for TC trajectory and intensity prediction. To model interactions between environmental fields, we design a Generative Adversarial Sequence Network integrating wind and geopotential height fields. For intra-field characteristics, a Wind Field Feature Cross-Fusion Module is introduced to capture dynamic wind-field correlations, and a Geopotential Height Spatiotemporal Feature Extraction Module is developed for evolutionary pattern analysis. Furthermore, a physics-informed loss grounded in fluid dynamics principles is incorporated to better characterize wind-field spatiotemporal variations. Experiments on the China Meteorological Administration Best Track Dataset (CMA-BST) demonstrate that the proposed method achieves superior trajectory and intensity prediction performance, particularly at 12 h and 24 h lead times. These results highlight the potential of integrating environmental-field fusion and physics-aware learning to advance next-generation TC prediction.

Graph Neural Networks with dilated convolutions for geomagnetic field forecasting: a single-station topological approach

Geomagnetic field forecasting is critical for mitigating space weather hazards, yet single-station prediction remains a challenge due to the complex, non-linear coupling of vector components. In this work, we propose a Graph Neural Network (GNN) architecture enhanced with Temporal Convolutional Networks (TCN) to forecast the H, D, and Z components. By modeling the observatory’s sensors as nodes in a learned directed graph, the system captures dynamic spatio-temporal correlations between orthogonal components. We introduce a dilated inception layer to efficiently capture multi-scale temporal patterns. Experimental results using 1-min downsampled data from the MAGDAS station (Ecuador) show that our model achieves a Mean Absolute Error (MAE) of 0.8036 nT, outperforming Vector Autoregression (VAR) and thoroughly optimized LSTM baselines. While the Naive Persistence baseline yields a marginally lower global MAE due to the statistical dominance of quiet-time periods, the proposed GNN-TCN provides vastly superior phase tracking ( R = 0.9950 ) and structural stability. Rigorous evaluation under varying space weather conditions reveals robust performance, maintaining a highly controlled error even during the top 5% most severe local geomagnetic storms. These findings, supported by power spectral density analysis, indicate that high-frequency fluctuations at a single station are dominated by instrumental and stochastic noise, making temporal filtering via downsampling essential. Ultimately, this proof-of-concept study demonstrates that utilizing a learned adjacency matrix as an adaptable structural regularization, rather than extracting a fixed physical law, provides a highly stable and effective framework for short-term geomagnetic field forecasting.

PhysAttNet: Enhancing Predictive Performance in Industrial and Astrophysical Time Series via Physics-Informed Attention

Accurate and robust time series forecasting is essential in many applications involving physical processes, such as manufacturing monitoring and astrophysical event detection. In these settings, predictive models must remain reliable under noise, variability, and measurement uncertainty while capturing temporally localized structures corresponding to physically meaningful events. Convolutional neural networks (CNNs) are widely used for such tasks due to their computational efficiency and strong representational capacity. However, their learned temporal representations often exhibit unstable or physically inconsistent attention patterns, reducing robustness, generalization, and interpretability. This paper introduces PhysAttNet, a physics-informed attention framework for time series forecasting. PhysAttNet augments a lightweight CNN forecaster with an attention head guided by domain-informed regularization reflecting the structural properties of physical signals. Specifically, three complementary constraints are imposed during training: an alignment regularization that encourages attention to follow smooth, peak-centered temporal structures derived from the input signal, a smoothness regularization that enforces continuous temporal evolution, and a sparsity regularization that promotes selective focus on informative intervals. These differentiable regularization terms introduce physics-guided inductive bias without requiring annotated explanations or manual supervision. Experiments on two distinct applications, namely predicting cutting forces during milling and forecasting flares in blazar time series, demonstrate that PhysAttNet improves forecasting accuracy, generalization, and prediction performance on structurally important events.

LoRA-EnVar: Parameter-Efficient Hybrid Ensemble Variational Assimilation for Weather Forecasting

Accurate estimation of background error (i.e., forecast error) distribution is critical for effective data assimilation (DA) in numerical weather prediction (NWP). In state-of-the-art operational DA systems, it is common to account for the temporal evolution of background errors by employing hybrid methods, which blend a static climatological covariance with a flow-dependent ensemble-derived component. While effective to some extent, these methods typically assume Gaussian-distributed errors and rely heavily on hand-crafted covariance structures and domain expertise, limiting their ability to capture the complex, non-Gaussian nature of atmospheric dynamics. In this work, we propose LoRA-EnVar, a novel hybrid ensemble variational DA algorithm that integrates low-rank adaptation (LoRA) into a deep generative modeling framework. We first learn a climatological background error distribution using a variational autoencoder (VAE) trained on historical data. To incorporate flow-dependent uncertainty, we introduce LoRA modules that efficiently adapt the learned distribution in response to flow-dependent ensemble perturbations. Our approach supports online finetuning, enabling dynamic updates of the background error distribution without catastrophic forgetting. We validate LoRA-EnVar in high-resolution assimilation settings using the FengWu forecast model and simulated observations from ERA5 reanalysis. Experimental results show that LoRA-EnVar significantly improves assimilation accuracy over models assuming static background error distribution and achieves comparable or better performance than full finetuning while reducing the number of trainable parameters by three orders of magnitude. This demonstrates the potential of parameter-efficient adaptation for scalable, non-Gaussian DA in operational meteorology