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 |
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Document Type: | Article |
Parent Title (German): | Journal of Computational Physics |
Volume: | 465 |
Year of first publication: | 2022 |
ArXiv Id: | http://arxiv.org/abs/2110.14523 |
DOI: | https://doi.org/10.1016/j.jcp.2022.111377 |