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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.00792 |
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| _version_ | 1866908624598597632 |
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| author | Banderwaar, Akshay Sai Gupta, Abhishek |
| author_facet | Banderwaar, Akshay Sai Gupta, Abhishek |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_00792 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fast PINN Eigensolvers via Biconvex Reformulation Banderwaar, Akshay Sai Gupta, Abhishek Machine Learning Artificial Intelligence Neural and Evolutionary Computing 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. |
| title | Fast PINN Eigensolvers via Biconvex Reformulation |
| topic | Machine Learning Artificial Intelligence Neural and Evolutionary Computing |
| url | https://arxiv.org/abs/2511.00792 |