Latent Spaces for Langevin Dynamics

In the field of machine learning coarse-grained potentials in molecular dynamics, many propagators require that the effective Hamiltonian is quadratic in momentum, thus limiting the family of coarse-graining functions. In this paper, we derive a general family of coarse-graining embedding functions for which Langevin dynamics samples correctly. These equations have significant implications for molecular simulations and pave the way for Langevin dynamics on non-geometric coarse-graining representations, such as those provided by principal components of component analysis or latent embeddings of molecules obtained from neural networks.