Deep learning the slow modes for rare events sampling

TL;DR

This paper introduces a machine learning-based method that uses neural networks to identify slow modes in systems from biased simulations, significantly improving the sampling of rare events in atomistic simulations.

Contribution

It presents a novel algorithm combining neural networks and on-the-fly enhanced sampling to extract transfer operator eigenfunctions from biased data, enabling efficient rare event sampling.

Findings

Successfully applied to small molecule conformational changes

Demonstrated effectiveness in mini-protein folding

Shown to accelerate materials crystallization simulations

Abstract

The development of enhanced sampling methods has greatly extended the scope of atomistic simulations, allowing long-time phenomena to be studied with accessible computational resources. Many such methods rely on the identification of an appropriate set of collective variables. These are meant to describe the system's modes that most slowly approach equilibrium. Once identified, the equilibration of these modes is accelerated by the enhanced sampling method of choice. An attractive way of determining the collective variables is to relate them to the eigenfunctions and eigenvalues of the transfer operator. Unfortunately, this requires knowing the long-term dynamics of the system beforehand, which is generally not available. However, we have recently shown that it is indeed possible to determine efficient collective variables starting from biased simulations. In this paper, we bring the power of machine learning and the efficiency of the recently developed on-the-fly probability enhanced sampling method to bear on this approach. The result is a powerful and robust algorithm that, given an initial enhanced sampling simulation performed with trial collective variables or generalized ensembles, extracts transfer operator eigenfunctions using a neural network ansatz and then accelerates them to promote sampling of rare events. To illustrate the generality of this approach we apply it to several systems, ranging from the conformational transition of a small molecule to the folding of a mini-protein and the study of materials crystallization.