Accurate forecasting of sea surface temperature (SST) and early detection of marine heatwave (MHW) events are critical yet challenging tasks due to the complex, nonlinear, and multiscale dynamics of the ocean-atmosphere system. To address these challenges, we propose a novel physics-guided hierarchical Transformer framework that combines deep spatiotemporal learning with physical process constraints. The architecture integrates a U-Net-style encoder-decoder with a Temporal-Spatial Predictor (TSP) module. It introduces a physics-constrained branch based on the mixed-layer heat budget equation, enhancing physical consistency and interpretability. A data-driven anomaly compensation mechanism is further employed to adaptively fuse physically-derived predictions with complex dynamic corrections through a learnable weighting scheme. This dual-stream architecture enables robust multi-step rolling forecasting and accurate detection of both gradual SST trends and abrupt MHW events. Extensive experiments on high-resolution SST datasets show that our model significantly outperforms state-of-the-art deep learning baselines such as ConvLSTM, DeepONet, FNO, and hybrid CNN-Transformer models across various performance metrics. These results highlight the framework’s ability to bridge physical oceanography and modern AI, providing a powerful tool for operational ocean forecasting and climate risk assessment.

This study presents a framework based on conditional diffusion probabilistic models for reconstructing vertical cloud structures from passive satellite remote sensing observations. The retrieval is formulated as a conditional denoising diffusion process, in which randomly initialized latent fields are progressively refined through iterative sampling guided by Moderate Resolution Imaging Spectroradiometer (MODIS) measurements. Compared with generative adversarial network (GAN)-based approaches, the proposed model more effectively captures the intrinsic variability, multiscale organization, and stochastic nature of atmospheric cloud fields. It exhibits superior performance in reconstructing complex multilayer systems, intense convective structures, and mesoscale cloud features. Quantitative evaluation against CloudSat radar reflectivity data demonstrates that the method consistently attains high structural similarity and accurately reproduces the vertical distribution of cloud reflectivity. These findings indicate that conditional diffusion probabilistic models provide a novel generative modeling paradigm for atmospheric remote sensing, providing physically consistent reconstructions, quantitative uncertainty characterization, and robust generalization to diverse atmospheric regimes. Furthermore, the framework can be extended to the three-dimensional reconstruction of other meteorological variables, supporting broader application of generative AI in satellite-based atmospheric analyses.

High-fidelity simulation and reconstruction of physical fields are essential in both scientific research and engineering, yet classical solvers can be prohibitively expensive at resolutions needed to capture fine-scale structures. We propose FNODiffSR, a data-driven super-resolution framework that couples a residual-guided diffusion model with an Adaptive Weighted Fourier Neural Operator (AWFNO). AWFNO models longrange spectral dependencies while selectively emphasizing highfrequency components, and the diffusion module employs a conditional probability-flow ODE instead of stochastic sampling to deterministically bridge low- and high-fidelity representations. Final reconstructions are obtained by integrating this ODE with an adaptive time-stepping solver. Experiments on quasigeostrophic turbulence across varied upsampling and sparsesampling regimes show that FNODiffSR consistently surpasses interpolation and learning-based baselines in reconstruction fidelity, structural similarity, and physical consistency (as assessed by a dimensionless equation-residual), while offering predictable runtime and scalability. These qualities make FNODiffSR a strong candidate for high-quality scientific data recovery and downstream analysis.

Accurate estimation of the background error covariance matrix denoted as B remains a critical challenge in numerical weather prediction (NWP), directly influencing data assimilation (DA) performance and forecast accuracy. Although hybrid ensemble-variational (EnVar) methods combine static and flow-dependent matrices to improve assimilation, their effectiveness is constrained by empirically fixed weights. To address this limitation, we propose DRL-EnVar, an adaptive hybrid EnVar DA method enhanced with deep reinforcement learning. DRL-EnVar integrates deep learning (DL) components, including a novel cyclic convolution module to extract abstract features from data, and employs reinforcement learning (RL) to dynamically optimize hybrid weighting strategies. The system adaptively combines multiple ensemble-based flow-dependent matrices with one or more static matrices to construct a time-varying hybrid matrix B that better reflects real-time background errors. Experimental results demonstrate that DRL-EnVar performs better than the traditional ensemble Kalman filter (EnKF) and hybrid covariance DA (HCDA) methods, especially under sparse observations or transitional changes in state variables. It achieves competitive or superior assimilation accuracy with lower computational cost, and can be flexibly integrated into both three-dimensional variational assimilation (3DVar) and four-dimensional variational assimilation (4DVar) frameworks. Overall, DRL-EnVar offers a novel and efficient approach to adaptive DA, particularly valuable for improving forecast skill during transitional weather regimes.

Precipitation nowcasting is a long-standing challenge due to the inherent unpredictability, which often lead to significant risks and damage. Traditional approaches that model nonlinear relationships between initial and future precipitation states often fail to accurately capture precipitation dynamics, including distribution and intensity patterns. Current data-driven methods are limited in their ability to represent the chaotic nature of precipitation without guidance from physical theory. To address this, we present Rainfusion, a generative model that integrates Prandtl’s mixing length theory from fluid dynamics with computer vision diffusion models. This integration accounts for nonlinear interactions between large-scale evolution and turbulent fluctuations in precipitation, generating physically plausible predictions. Rainfusion significantly improves forecasting skill on two benchmark dataset over the next 3 hours. Furthermore, we enhance Rainfusion with a control network trained on multi-source data, particularly lightning observations, enabling more accurate and controllable predictions of precipitation’s spatial-temporal patterns. Weather forecasters can utilize Rainfusion to guide predictions toward either growth or decay based on their domain expertise. Our approach advances precipitation nowcasting, offering a robust framework that bridges physical theory with modern deep learning techniques.

Quantitative precipitation nowcasting (QPN) is a highly challenging task in weather forecasting. The ability to provide precise, immediate, and detailed QPN products is necessary for a variety of situations, including storm warnings, air travel, and large gatherings. To address this challenge, this article proposes a new transformer lightweight physics-informed transformer (LPT)-QPN for QPN tasks, utilizing vertical cumulative liquid water content (VIL) products. This model adopts novel transformer modules to model the long-term evolution of precipitation and incorporates multihead squared attention (MHSA) to model its highly nonlinear relationships while reducing computational complexity. The results of experimental evaluations demonstrate the superiority of LPT-QPN when compared to existing state-of-the-art QPN models. In particular, the LPT-QPN model demonstrates greater accuracy for long lead time and in high-intensity areas, confirmed in both quantitative and qualitative evaluations. In addition, through three customized fine-tuning schemes, we are able to further improve the predictability of the LPT-QPN model for specific precipitation events. By incorporating the physical constraints of the convection-diffusion equation, our approach offers novel perspectives for future explorations that combine physical prior knowledge and deep-learning (DL) techniques.

The accuracy of the initial field is crucial to the forecast results of numerical weather prediction (NWP). Data assimilation (DA) is a method to provide the initial field to the NWP. Currently, the hybrid 4DVar-EnKF DA method is the primary DA method used by operational NWP centres. The technique requires the derivation of the tangent linear and adjoint models for the nonlinear model, but it’s challenging to get the tangent linear and the adjoint models. Furthermore, this method usually adopts empirical coefficients to combine the four-dimensional variational assimilation (4DVar) and the ensemble Kalman filter (EnKF), which reduces the accuracy of assimilation results. This paper builds a hybrid DA system based on a deep learning model (DL-HDA) in response to the above problems. First, we establish a forecast model based on the bilinear neural network (BNN) and use the tangent linear and adjoint models of the BNN for the 4DVar. Then, we utilize the ResNet model to combine the analysis of the 4DVar and the EnKF. The experiments are carried out on the Lorenz-96 model, and then the DL-HDA is compared with the traditional method. The experimental results show that the DL-HDA can improve the precision of assimilation results and decrease the system’s running time.

The quality and accuracy of Numerical Weather Prediction (NWP) is based on its initial conditions (ICs), boundary conditions and forecast models. Data assimilation (DA) is a crucial procedure to optimally estimate the actual atmospheric state (known as the analysis field) as ICs for NWP by integrating available information, including the observation and the background field. Instead of only focusing on the speed-up for DA in virtue of the customized neural networks, this paper exploratively introduces the spatial-temporal peculiarities to construct a new hybrid data assimilation approach based on multilayer perceptron (MLP); and, its effectiveness and validity are verified in two classical nonlinear dynamic models. The results of experiments demonstrate that the Cache-MLP generally produces similar or smaller root mean square errors (RMSE) with much less time consuming, compared to the conventional 3D-Var and EnKF DA methods, and noticeably, the Cache-MLP has a more robust representation of turning points in the trajectories of the state variables. The final Backtracked-MLP learns appropriate weight matrix to couple previous two traditional DA methods and increases the accuracy by 10.32% in the Lorenz-63 system while 14.03% in the Lorenz-96 system, in comparison with the empirical hybrid DA method. To some extent, this method could be a reference to further researches to optimize the quality of the analysis field, in the meantime, saving significant computing time and resources by deep learning.

Several ensemble-based three-dimensional variational (3D-Var) filters are compared. These schemes replace the static background error covariance of the traditional 3D-Var with the ensemble forecast error covariance, but generate analysis ensemble anomalies (perturbations) in different ways. However, it is demonstrated in this paper that they are all theoretically equivalent to the ensemble transformation Kalman filter (ETKF). Furthermore, a new method named EnPSAS is presented. The analysis shows that EnPSAS has a small condition number and can apply covariance localization more easily than other ensemble-based 3D-Var methods.

QoS routing and multipath routing have been receiving much attention respectively in network communication. However, the research combining those two kinds of routing is rare. This paper integrated the ideas of QoS and multipath, and presented the problem of Shortest Pair of Disjoint Paths with Bandwidth Guaranteed. We proved it to be NP-Complete, and then proposed a heuristic algorithm. The analysis indicates that our algorithm shows good performance and it can produce optimal solutions in most cases.

Multipath Routing plays an important role in communication networks. Multiple disjoint paths can increase the effective bandwidth between pairs of vertices, avoid congestion in a network and reduce the probability of dropped packets. In this paper, we built mathematical models for arc-disjoint paths problem and vertex-disjoint paths problem respectively, and then proposed polynomial algorithms for finding the shortest pair of arc and vertex-disjoint paths, both with the time complexity of O(m). Furthermore, we extend these algorithms to find any k disjoint paths in time O(km), whose sum-weight is minimized.