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

TL;DR

This paper introduces a physics-informed generative solver that combines stable prior learning with enforcement of physical laws, enabling accurate reconstruction of physical fields from sparse data in various domains.

Contribution

It presents a novel framework that separates prior learning from physics-based inference, ensuring stability and adherence to conservation laws without retraining.

Findings

Successfully reconstructs acoustic fields from sparse sensors, reducing spatial aliasing.

Generalizes to meteorological data with extreme sparsity, demonstrating robustness.

Establishes a new paradigm bridging AI generative models and physical science.

Abstract

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.