Fast PINN Eigensolvers via Biconvex Reformulation
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Abstract (arXiv)
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× faster than gradient-based PINN training. We release our codes at https://github.com/NeurIPS-ML4PS-2025/PINNACSCODES.
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References · 16
- 2020Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domainscited by 2,170
- 2021Characterizing possible failure modes in physics-informed neural networkscited by 632
- 2024Weak baselines and reporting biases lead to overoptimism in machine learning for fluid-related partial differential equationscited by 87
- 2021Multi-Objective Loss Balancing for Physics-Informed Deep Learningcited by 86
- 2024From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learningcited by 73
- 2024PirateNets: Physics-informed Deep Learning with Residual Adaptive Networkscited by 70
- 2023Can Physics-Informed Neural Networks beat the Finite Element Method?cited by 68
- 2021Learning in Sinusoidal Spaces with Physics-Informed Neural Networkscited by 61
- 2020Deep Randomized Neural Networkscited by 33
- 2021On Computing the Hyperparameter of Extreme Learning Machines: Algorithm and Application to Computational PDEs, and Comparison with Classical and High-Order Finite Elementscited by 25
- 2022On the Role of Fixed Points of Dynamical Systems in Training Physics-Informed Neural Networkscited by 23
- 2022A Method for Computing Inverse Parametric PDE Problems with Random-Weight Neural Networkscited by 14
4 more
- 2025Evolutionary Optimization of Physics-Informed Neural Networks: Evo-PINN Frontiers and Opportunitiescited by 10
- 2025Solving engineering eigenvalue problems with neural networks using the Rayleigh quotientcited by 8
- 2022Neuroevolution of Physics-Informed Neural Nets: Benchmark Problems and Comparative Resultscited by 4
- 2020How Powerful are Shallow Neural Networks with Bandlimited Random Weights?cited by 3
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