{"ID":2846941,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.00792","arxiv_id":"2511.00792","title":"Fast PINN Eigensolvers via Biconvex Reformulation","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.","short_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 numer...","url_abs":"https://arxiv.org/abs/2511.00792","url_pdf":"https://arxiv.org/pdf/2511.00792v1","authors":"[\"Akshay Sai Banderwaar\",\"Abhishek Gupta\"]","published":"2025-11-02T04:04:54Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.AI\",\"cs.NE\"]","methods":"[]","has_code":false,"code_links":[{"ID":607472,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_id":2846941,"paper_url":"https://arxiv.org/abs/2511.00792","paper_title":"Fast PINN Eigensolvers via Biconvex Reformulation","repo_url":"https://github.com/NeurIPS-ML4PS-2025/PINN_ACS_CODES","is_official":false,"mentioned_in_paper":false,"mentioned_in_github":true,"github_stars":0}]}