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

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