Work

Deep Eigenspace Network for Parametric Non-self-adjoint Eigenvalue Problems

Year: 2025

Type: preprint

Abstract: We consider operator learning for efficiently solving parametric non-self-adjoint eigenvalue problems. To overcome the spectral instability and mode switching associated with non-self-adjoint operators, we choose to learn the eigenspace rather than individual eigenfunctions. In particular, we propose a Deep Eigenspace Network (DEN) architecture integrating Fourier Neural Operators, geometry-adaptive POD bases, and explicit banded cross-mode mixing mechanism to capture complex spectral dependencies. We apply DEN to the non-self-adjoint Steklov eigenvalue problem and prove the Lipschitz continuity of the eigenspace with respect to the parameter. Furthermore, we derive error bounds for the eigenvalues. Numerical experiments validate that DEN is highly effective and efficient.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2512.20058

Authors: Li, H., Sun, J., Zhang, Z.

Institutions: University of Hong Kong, Michigan Technological University

Topic: Model Reduction and Neural Networks

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, National Natural Science Foundation of China

Award: Novel Finite Element Methods for Nonlinear Eigenvalue Problems - A Holomorphic Operator-Valued Function Approach

OpenAlex ID: W7117259686

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