Physics-Informed Generative Solver: Bridging Data-Driven Priors and Conservation Laws for Stable Spatiotemporal Field Reconstruction

Reconstructing continuous physical fields from sparse measurements is a central inverse problem, but data-driven generative models can produce states that violate governing dynamics. We introduce a physics-informed generative solver that separates stable prior learning from inference-time enforcement of conservation laws. Martingale-Regularized Score Matching regularizes score pretraining with a Score Fokker-Planck constraint, yielding a dynamically stable prior. Physics-Informed Implicit Score Sampling then guides denoising trajectories by gradients of physical residuals, projecting samples toward admissible manifolds without retraining. In acoustics, the method co-generates pressure and particle velocity from sparse sensors, enabling dense virtual arrays that suppress spatial aliasing. The same framework generalizes to real-world ERA5 meteorological fields under extreme sparsity. Together, this work establishes a rigorous and generalizable paradigm for solving high-dimensional inverse problems, bridging the gap between generative artificial intelligence and first-principles science.

TRUST-FS: Tensorized Reliable Unsupervised Multi-View Feature Selection for Incomplete Data

Multi-view unsupervised feature selection (MUFS), which selects informative features from multi-view unlabeled data, has attracted increasing research interest in recent years. Although great efforts have been devoted to MUFS, several challenges remain: 1) existing methods for incomplete multi-view data are limited to handling missing views and are unable to address the more general scenario of missing variables, where some features have missing values in certain views; 2) most methods address incomplete data by first imputing missing values and then performing feature selection, treating these two processes independently and overlooking their interactions; 3) missing data can result in an inaccurate similarity graph, which reduces the performance of feature selection. To solve this dilemma, we propose a novel MUFS method for incomplete multi-view data with missing variables, termed Tensorized Reliable UnSupervised mulTi-view Feature Selection (TRUST-FS). TRUST-FS introduces a new adaptive-weighted CP decomposition that simultaneously performs feature selection, missing-variable imputation, and view weight learning within a unified tensor factorization framework. By utilizing Subjective Logic to acquire trustworthy cross-view similarity information, TRUST-FS facilitates learning a reliable similarity graph, which subsequently guides feature selection and imputation. Comprehensive experimental results demonstrate the effectiveness and superiority of our method over state-of-the-art methods.