Physics-Informed Generative Solver: Bridging Data-Driven Priors and Conservation Laws for Stable Spatiotemporal Field Reconstruction
Organizations: School of Advanced Manufacturing Engineering, Nanjing University, Suzhou, 215163, China. · National Laboratory of Solid State Microstructures, Nanjing University, Nanjing, 210093, China. · Suzhou Acoustics Industry Technology Research Institute Co., Ltd., Suzhou, 215513, China. · School of Mechanical and Electric Engineering, Soochow University, Suzhou, 215131, China. · Shishan Laboratory, Nanjing University, Suzhou, 215163, China. · Jiangsu Key Laboratory of Quantum Information Science and Technology, Nanjing University, Suzhou 215163, China. · Key Laboratory of Nanodevices and Applications, Suzhou Institute of Nano-tech and Nano-bionics, Chinese Academy of Sciences, Suzhou, 215125, China. · National Key Laboratory of Helicopter Aeromechanics, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China. · Key Laboratory of Noise and Vibration Research, Institute of Acoustics, Chinese Academy of Sciences, Beijing, 100190, China. · Jiangsu Key Laboratory of Artificial Functional Materials, Nanjing, 210093, China. · Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, 210093, China.
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.