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

TL;DR

Eig-PIELM is a mesh-free, physics-informed machine learning framework that efficiently solves linear eigenvalue problems with high accuracy, suitable for rapid parametric analysis in engineering systems.

Contribution

The paper introduces Eig-PIELM, a novel mesh-free approach that reformulates eigenvalue problems into a single algebraic system with exact boundary condition enforcement, enhancing efficiency and accuracy.

Findings

Demonstrated robustness and accuracy on benchmark problems.

Achieved simultaneous eigenvalues and mode shapes in one solve.

Eliminated penalty parameters and backpropagation overhead.

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.