Deep Representation Learning for Complex Free-Energy Landscapes.

In this Letter, we analyzed the inductive bias underlying complex free-energy landscapes (FELs) and exploited it to train deep neural networks that yield reduced and clustered representation for the FEL. Our parametric method, called information distilling of metastability (IDM), is end-to-end differentiable and thus scalable to ultralarge data sets. IDM is able to perform clustering in the meantime of reducing the dimensionality. Besides, as an unsupervised learning method, IDM differs from many existing dimensionality reduction and clustering methods in that it requires neither a cherry-picked distance metric nor the ground-true number of clusters defined a priori, and it can be used to unroll and zoom in on the hierarchical FEL with respect to different time scales. Through multiple experiments, we show that IDM can achieve physically meaningful representations that partition the FEL into well-defined metastable states that hence are amenable for downstream tasks such as mechanism analysis and kinetic modeling.