Fast PINN Eigensolvers via Biconvex Reformulation
This addresses a computational bottleneck for researchers and engineers using PINNs in physics and engineering applications, though it is an incremental improvement over existing PINN methods.
The paper tackles the slow convergence of Physics-Informed Neural Networks (PINNs) for eigenvalue problems by reformulating them as a biconvex optimization, achieving up to 500x faster convergence than gradient-based PINN training.
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.