Nonlinear machine learning in simulations of soft and biological materials

Interpretable parameterisations of free energy landscapes for soft and biological materials calculated from molecular simulation require the availability of ‘good’ collective variables (CVs) capable of discriminating the metastable states of the system and the barriers between them. If these CVs are coincident with the slow collective modes governing the long-time dynamical evolution, then they also furnish good coordinates in which to perform enhanced sampling to surmount high free energy barriers and efficiently explore and recover the landscape. Non-linear manifold learning techniques provide a means to systematically extract such CVs from molecular simulation trajectories by identifying and extracting low-dimensional manifolds lying latent within the high-dimensional coordinate space. We survey recent advances in data-driven CV discovery and enhanced sampling using non-linear manifold learning, describe the mathematical and theoretical underpinnings of these techniques, and present illustrative examples to molecular folding and colloidal self-assembly. We close with our outlook and perspective on future advances in this rapidly evolving field.