[2509.02617] Gaussian process surrogate with physical law-corrected prior for multi-coupled PDEs defined on irregular geometry

Statistics > Machine Learning arXiv:2509.02617 (stat) [Submitted on 1 Sep 2025 (v1), last revised 7 Apr 2026 (this version, v2)] Title:Gaussian process surrogate with physical law-corrected prior for multi-coupled PDEs defined on irregular geometry Authors:Pucheng Tang, Hongqiao Wang, Wenzhou Lin, Qian Chen, Heng Yong View a PDF of the paper titled Gaussian process surrogate with physical law-corrected prior for multi-coupled PDEs defined on irregular geometry, by Pucheng Tang and 3 other authors View PDF HTML (experimental) Abstract:Parametric partial differential equations (PDEs) serve as fundamental mathematical tools for modeling complex physical phenomena, yet repeated high-fidelity numerical simulations across parameter spaces remain computationally prohibitive. In this work, we propose a physical law-corrected prior Gaussian process (LC-prior GP) for efficient surrogate modeling of parametric PDEs. The proposed method employs proper orthogonal decomposition (POD) to represent high-dimensional discrete solutions in a low-dimensional modal coefficient space, significantly reducing the computational cost of kernel optimization compared with standard GP approaches in full-order spaces. The governing physical laws are further incorporated to construct a law-corrected prior to overcome the limitation of existing physics-informed GP methods that rely on linear operator invariance, which enables applications to nonlinear and multi-coupled PDE systems without kernel redesign...