Interpretation of autoencoder-learned collective variables using Morse-Smale complex: an application on molecular trajectories

Nonlinear dimension reduction is a key step towards a minimalist yet accurate understanding of physical systems. A number of methods based on data science and machine learning have shown great promise to automate the process. However, the physical meaning of the automatically-discovered collective variables (CVs) is mostly elusive. In this work, we constructed a framework that 1. determines the optimal number of CVs capturing essential molecular motions using an ensemble of hierarchical autoencoders, and 2. interpreted the physical meanings of the CVs learned by a traditional autoencoder with Morse-Smale (MS) complex and sublevelset persistence homology. We demonstrated this approach with several small molecular systems. This work can be considered as an explainable nonlinear dimensionality reduction method.