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.

我们提出了得分动力学（SD）作为从分子动力学（MD）模拟中学习高效演化算子的通用框架。我们构建了基于图神经网络的得分动力学模型，用于真实分子系统的演化，演化时间步长为1个皮秒，并通过丙氨酸二肽和溶液中的短链烷烃的案例研究展示了得分动力学的性能。相比于MD，得分动力学在平衡预测和动力学预测上具有8-18倍的计算速度提升，并讨论了改进得分动力学的挑战和可能的未来解决方案。

分数动力学：通过条件扩散模型缩放皮秒级分子动力学