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Solving eigenvalue PDEs of metastable diffusion processes using artificial neural networks

  • In this paper, we consider the eigenvalue PDE problem of the infinitesimal generators of metastable diffusion processes. We propose a numerical algorithm based on training artificial neural networks for solving the leading eigenvalues and eigenfunctions of such high-dimensional eigenvalue problem. The algorithm is useful in understanding the dynamical behaviors of metastable processes on large timescales. We demonstrate the capability of our algorithm on a high-dimensional model problem, and on the simple molecular system alanine dipeptide.
Author:Wei Zhang, Tiejun Li, Christof Schütte
Document Type:Article
Parent Title (German):Journal of Computational Physics
Year of first publication:2022
ArXiv Id:http://arxiv.org/abs/2110.14523
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