The dynamics of a 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, 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.

本文研究了深度学习算法在构建高维次稳态分子系统的共同变量及其有效模拟中的应用，在基于无穷小生成器或转移算子与基础动力学相关的领先特征函数计算或通过最小化重构误差来学习自动编码器之间提出了一个简洁的概述，并在说明性示例上对这两种方法进行了比较的数值研究