# Solving eigenvalue PDEs of metastable diffusion processes using artificial neural networks

arXiv: https://arxiv.org/abs/2110.14523 · HTML: https://mlsanity.com/paper/2110.14523/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Oct 2021.

## Built on by (most cited first, 13 of 13)

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## Abstract (arXiv)

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 able to find multiple leading eigenpairs by solving a single training task. It 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.