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We propose score dynamics, a general framework for learning acceleratedevolution operators with large timesteps from molecular-dynamics simulations.SD is centered around scores, or derivatives of the transition log-probabilitywith respect to the dynamical degrees of freedom. The latter play the same roleas force fields in MD but are used in denoising diffusion probability models togenerate discrete transitions of the dynamical variables in an SD timestep,which can be orders of magnitude larger than a typical MD timestep. In thiswork, we construct graph neural network based score dynamics models ofrealistic molecular systems that are evolved with 10 ps timesteps. Wedemonstrate the efficacy of score dynamics with case studies of alaninedipeptide and short alkanes in aqueous solution. Both equilibrium predictionsderived from the stationary distributions of the conditional probability andkinetic predictions for the transition rates and transition paths are in goodagreement with MD. Our current SD implementation is about two orders ofmagnitude faster than the MD counterpart for the systems studied in this work.Open challenges and possible future remedies to improve score dynamics are alsodiscussed.

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