Eig-PIELM: A Mesh-Free Approach for Efficient Eigen-Analysis with Physics-Informed Extreme Learning Machines
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866918352114417664 |
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| author | Mishra, Rishi Smriti Krishnamurthi, Ganapathy Srinivasan, Balaji Natarajan, Sundararajan |
| author_facet | Mishra, Rishi Smriti Krishnamurthi, Ganapathy Srinivasan, Balaji Natarajan, Sundararajan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_15343 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Eig-PIELM: A Mesh-Free Approach for Efficient Eigen-Analysis with Physics-Informed Extreme Learning Machines Mishra, Rishi Smriti Krishnamurthi, Ganapathy Srinivasan, Balaji Natarajan, Sundararajan Numerical Analysis 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. |
| title | Eig-PIELM: A Mesh-Free Approach for Efficient Eigen-Analysis with Physics-Informed Extreme Learning Machines |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2508.15343 |