Understanding recent deep-learning techniques for identifying collective variables of molecular dynamics

TL;DR

This paper reviews and compares deep learning methods for identifying collective variables in molecular dynamics, focusing on eigenfunction computation and autoencoder learning, to improve modeling of complex molecular systems.

Contribution

It provides a concise overview of two main deep learning approaches for CV identification and compares their performance through numerical experiments.

Findings

Eigenfunction-based methods effectively capture slow dynamics.

Autoencoders excel in reconstructing molecular configurations.

Comparative analysis highlights strengths and limitations of each approach.

Abstract

High-dimensional metastable molecular system can often be characterised by a few features of the system, i.e. collective variables (CVs). Thanks to the rapid advance in the area of machine learning and deep learning, various deep learning-based CV identification techniques have been developed in recent years, allowing accurate modelling and efficient simulation of complex molecular systems. In this paper, we look at two different categories of deep learning-based approaches for finding CVs, either by computing leading eigenfunctions of infinitesimal generator or transfer operator associated to the underlying dynamics, or by learning an autoencoder via minimisation of reconstruction error. We present a concise overview of the mathematics behind these two approaches and conduct a comparative numerical study of these two approaches on illustrative examples.