用物理定律约束生成模型，让稀疏数据也能重建稳定物理场。
Physics-Informed Generative Solver: Bridging Data-Driven Priors and Conservation Laws for Stable Spatiotemporal Field Reconstruction
- 先学稳定先验，再推理时用物理残差引导采样。
- 在声学中仅用稀疏传感器就重建出完整压力与速度场。
- 适合需要物理一致性高精度重建的科研与工程场景。
从稀疏测量中重建连续物理场是核心逆问题，但数据驱动生成模型可能违背基本动力学规律。本文提出一种物理信息生成求解器，将稳定先验学习与推理阶段的守恒律强制分离。通过马丁格尔正则化得分匹配引入得分福克-普朗克约束，获得动态稳定的先验分布；再通过物理信息隐式得分采样，利用物理残差梯度引导去噪轨迹，将样本投影至可接受流形，无需重新训练。在声学场景中，该方法仅需稀疏传感器即可联合生成压力与粒子速度场，实现密集虚拟阵列，有效抑制空间混叠。同一框架可推广至极端稀疏条件下的真实世界ERA5气象场重建。本工作建立了高维逆问题求解的严格且可推广范式，弥合了生成人工智能与第一性原理科学之间的鸿沟。
原文摘要 · Abstract (English)
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.
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