AI RESEARCH
Deep Eigenspace Network for Parametric Non-self-adjoint Eigenvalue Problems
arXiv CS.LG
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ArXi:2512.20058v2 Announce Type: replace-cross 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.