用流匹配方法实现任意稀疏传感器下的物理参数快速反演
PIS: A Generalized Physical Inversion Solver for Arbitrary Sparse Observations via Set Conditioned Flow Matching
- 基于集合条件流匹配与稀疏性课程学习，实现非规则传感器数据反演
- 极端稀疏下（<1%）误差降低88.7%，推理仅需50次函数求值
- 适合高维物理建模、传感器优化与不确定性量化场景
从有限且间接的测量中估计受偏微分方程约束的高维物理参数是一个高度病态的问题。传统方法在观测稀疏、不规则采样及真实传感器布设限制下面临精度与效率瓶颈。我们提出物理反演求解器（PIS），将集合条件流匹配与余弦退火稀疏性课程（CASC）相结合，实现对任意非网格传感器数据的稳定反演，即使在极小引导下亦可完成。通过直线路径传输，PIS 实现瞬时推理（50 NFEs），相比迭代基线提速数量级。大量实验表明，PIS 在地下特征刻画、波基表征与结构健康监测任务中，极端稀疏条件下（<1%）误差降低达88.7%，并提供稳健的不确定性量化以指导最优传感器布局。
原文摘要 · Abstract (English)
The estimation of high-dimensional physical parameters constrained by partial differential equations (PDEs) from limited and indirect measurements is a highly ill-posed problem. Traditional methods face significant accuracy and efficiency bottlenecks, particularly when observations are sparse, irregularly sampled, and constrained by real-world sensor placement. We propose the Physical Inversion Solver (PIS), a unified framework that couples Set-Conditioned Flow Matching with a Cosine-Annealed Sparsity Curriculum (CASC) to enable stable inversion from arbitrary, off-grid sensors even under minimal guidance. By leveraging straight-path transport, PIS achieves instantaneous inference (50 NFEs), offering orders-of-magnitude speedup over iterative baselines. Extensive experiments demonstrate that PIS reduces error by up to 88.7% under extreme sparsity (<1%) across subsurface characterization, wave-based characterization, and structural health monitoring, while providing robust uncertainty quantification for optimal sensor placement.
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