
























Authors:Ziyuan Zhu, Keyu Hu, Zhifei Chen, Yuhao Shi, Ming Bao, Jing Zhao, Gang Wang, Haitan Xu, Jiadong Li, Qijun Zhao, Xiaodong Li, Minghui Lu, Yanfeng Chen
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.
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2605.22338 [cs.LG] |
| (or arXiv:2605.22338v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.22338 arXiv-issued DOI via DataCite (pending registration) |
From: Ziyuan Zhu [view email]
[v1]
Thu, 21 May 2026 11:24:48 UTC (11,964 KB)
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