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.

翻译：高阶亚稳态分子系统通常可用系统的少数特征（即集体变量）来表征。得益于机器学习和深度学习领域的快速发展，近年来涌现出多种基于深度学习的集体变量识别技术，使得复杂分子系统的精确建模与高效模拟成为可能。本文探讨了两类基于深度学习的集体变量识别方法：一类通过计算与底层动力学相关的无穷小生成元或传递算子的主导本征函数来实现，另一类通过最小化重构误差来学习自编码器。我们简明扼要地阐述了这两类方法背后的数学原理，并通过说明性示例对它们进行了对比数值研究。