Solving eigenvalue PDEs of metastable diffusion processes using artificial neural networks

Understand

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.