Solving eigenvalue PDEs of metastable diffusion processes using artificial neural networks
arXiv:2110.14523 · doi:10.1016/j.jcp.2022.111377
Abstract
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.
arXiv commentrevision with minor changes
References in corpus (22)
- Escaping free-energy minima
- A Data-Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition
- Simulated Tempering: A New Monte Carlo Scheme
- Solving high-dimensional partial differential equations using deep learning
- Identification of slow molecular order parameters for Markov model construction
- Applied Koopmanism
- Deep neural network solution of the electronic Schrödinger equation
- Ab-Initio Solution of the Many-Electron Schrödinger Equation with Deep Neural Networks
- Data-driven model reduction and transfer operator approximation
- Molecular enhanced sampling with autoencoders: On-the-fly collective variable discovery and accelerated free energy landscape exploration
- Machine learning force fields and coarse-grained variables in molecular dynamics: application to materials and biological systems
- Solving Many-Electron Schrödinger Equation Using Deep Neural Networks
- Nonlinear Discovery of Slow Molecular Modes using State-Free Reversible VAMPnets
- Artificial Neural Network Methods in Quantum Mechanics
- Variance Reduction using Nonreversible Langevin Samplers
- Solving high-dimensional eigenvalue problems using deep neural networks: A diffusion Monte Carlo like approach
- Computing Committor Functions for the Study of Rare Events Using Deep Learning
- Interpolating between BSDEs and PINNs: deep learning for elliptic and parabolic boundary value problems
- Constraint-Based Regularization of Neural Networks
- Multiple projection MCMC algorithms on submanifolds
- Non-convex Conditional Gradient Sliding
- A Priori Generalization Error Analysis of Two-Layer Neural Networks for Solving High Dimensional Schrödinger Eigenvalue Problems