Eig-PIELM: A Mesh-Free Approach for Efficient Eigen-Analysis with Physics-Informed Extreme Learning Machines

2025/08/21 by Mishra, Rishi, Smriti, Krishnamurthi, Ganapathy +2 · 2 citations
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2508.15343

Abstract

In this work, a novel Eig-PIELM framework is proposed that extends physics-informed extreme learning machine for an efficient and accurate solution of linear eigenvalue problems. The method reformulates the governing differential equations into a compact algebraic system solvable in a single step. Boundary conditions are enforced exactly via an algebraic projection onto the boundary-admissible subspace, eliminating the computational overhead of penalty parameters, and backpropagation while preserving the computational advantages of extreme learning machines. The proposed framework is mesh-free and yields both eigenvalues and mode shapes simultaneously in one linear solve. The robustness and accuracy of the proposed framework is demonstrated through a range of benchmark problems. We believe that the mesh-free nature, solution structure and accuracy of Eig-PIELM makes it particularly valuable for parametric studies in mechanical, acoustic, and electromechanical systems where rapid frequency spectrum analysis is critical.

Citations

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Cited by

• Fast PINN Eigensolvers via Biconvex Reformulation
• General Fourier Feature Physics-Informed Extreme Learning Machine (GFF-PIELM) for High-Frequency PDEs

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