Fast PINN Eigensolvers via Biconvex Reformulation

📝 Original Info

• Title: Fast PINN Eigensolvers via Biconvex Reformulation
• ArXiv ID: 2511.00792
• Date: 2025-11-02
• Authors: 저자 정보가 제공되지 않았습니다. (논문에 명시된 저자 목록이 없으므로, 추후 확인 필요)

📝 Abstract

Eigenvalue problems have a distinctive forward-inverse structure and are fundamental to characterizing a system's thermal response, stability, and natural modes. Physics-Informed Neural Networks (PINNs) offer a mesh-free alternative for solving such problems but are often orders of magnitude slower than classical numerical schemes. In this paper, we introduce a reformulated PINN approach that casts the search for eigenpairs as a biconvex optimization problem, enabling fast and provably convergent alternating convex search (ACS) over eigenvalues and eigenfunctions using analytically optimal updates. Numerical experiments show that PINN-ACS attains high accuracy with convergence speeds up to 500$\times$ faster than gradient-based PINN training. We release our codes at https://github.com/NeurIPS-ML4PS-2025/PINN_ACS_CODES.

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