Score dynamics: scaling molecular dynamics with picosecond timesteps via conditional diffusion model

We propose score dynamics (SD), a general framework for learning effective evolution operators for atomistic as well as coarse-grained dynamics from molecular-dynamics (MD) simulations. SD is centered around scores, or derivatives of the transition log-probability with respect to the dynamical degrees of freedom. The latter play the same role as force fields in MD but are used in denoising diffusion probability models to generate discrete transitions of the dynamical variables in an SD timestep, which can be orders of magnitude larger than a typical MD timestep. In this work, we construct graph neural network based score dynamics models of realistic molecular systems that are evolved with 1~ps timesteps. We demonstrate the efficacy of score dynamics with case studies of alanine dipeptide and short alkanes in aqueous solution. Both equilibrium predictions derived from the stationary distributions of the conditional probability and kinetic predictions for the transition rates and transition paths are in good agreement with MD at about 8-18 fold wall-clock speedup. Open challenges and possible future remedies to improve score dynamics are also discussed.