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.

Partial differential equations (PDEs) are indispensable tools for conducting scientific research in a variety of disciplines and play a vital role in fields such as meteorology, oceanography, and biology. These powerful mathematical tools enable scientists and researchers to describe and analyze complex phenomena. However, it is often difficult to obtain exact analytical solutions of PDEs, and the numerical methods for solving PDEs are often computationally intensive and time-consuming. In recent years, with the continuous research on deep learning, physics-informed neural networks (PINNs) have been successfully applied to find numerical solutions of PDEs and have shown great potential. Meanwhile, solitary waves have also attracted great interest from researchers in nonlinear science. In this paper, we use the improved PINNs to numerically simulate the solitary wave solutions of PDEs. The improved PINNs not only incorporate constraints on the control equations to ensure the interpretability of the prediction results, which is important for physical field simulations. In addition, an adaptive activation function is introduced. In this paper, the Sawada-Kotera equation and the Caudrey-Dodd-Gibbon-Sawada-Kotera (CDGSK) equation are selected for study and the accuracy of the predicted solitary wave solution is evaluated by analyzing the error of the simulation results. The experimental results show that the improved PINNs significantly outperform the original PINNs with shorter training time and more accurate prediction results.

Partial differential equations (PDEs) are fundamental tools for studying complex systems. However, the methods for solving PDEs are typically complex. Currently, numerical methods are commonly used to simulate the evolution of complex systems governed by PDEs. Nevertheless, these numerical methods often require significant computational resources and are time-consuming. In recent years, deep learning techniques, specifically Physics Informed Neural Networks (PINNs), have gained attention in the scientific community. PINNs have shown promising results in solving PDEs and simulating physical fields. In this study, the improved PINNs incorporate the constraints of PDEs and gradient information, enhancing the interpretability of the neural network model. Furthermore, an adaptive learning method is employed to update the weight coefficients of the loss function and dynamically adjust the ratio of each constraint term, resulting in accelerated training speed. Rogue waves are of significant research value in the field of nonlinear science and have found applications in various domains. In the experiment, we apply the improved PINNs to numerically simulate rogue wave solutions of PDEs. We evaluate the accuracy of the rogue wave simulation by conducting the error analysis of the results. The experimental results demonstrate that the improved PINNs outperform traditional PINNs in terms of training efficiency and prediction accuracy for rogue wave simulations.