Coarse-Grained Molecular Dynamics with Normalizing Flows

We propose a sampling algorithm relying on a collective variable (CV) of midsize dimension modeled by a normalizing flow and using nonequilibrium dynamics to propose full configurational moves from the proposition of a refreshed value of the CV made by the flow. The algorithm takes the form of a Markov chain with nonlocal updates, allowing jumps through energy barriers across metastable states. The flow is trained throughout the algorithm to reproduce the free energy landscape of the CV. The output of the algorithm is a sample of thermalized configurations and the trained network that can be used to efficiently produce more configurations. We show the functioning of the algorithm first in a test case with a mixture of Gaussians. Then, we successfully tested it on a higher-dimensional system consisting of a polymer in solution with a compact state and an extended stable state separated by a high free energy barrier.