The equations of classical mechanics can be used to model the time evolution of countless physical systems, from the astrophysical to the atomic scale. Accurate numerical integration requires small time steps, which limits the computational efficiency -- especially in cases such as molecular dynamics that span wildly different time scales. Using machine-learning (ML) algorithms to predict trajectories allows one to greatly extend the integration time step, at the cost of introducing artifacts such as lack of energy conservation and loss of equipartition between different degrees of freedom of a system. We propose learning data-driven structure-preserving (symplectic and time-reversible) maps to generate long time-step classical dynamics and show that this method is equivalent to learning the mechanical action of the system of interest. These models can be learned based on short reference trajectories, and be transferred across thermodynamic conditions and chemical composition. We show that an action-derived ML integrator eliminates the pathological behavior of non-structure-preserving ML predictors, and that the method can be applied iteratively, serving as a correction to computationally cheaper direct predictors.

翻译：经典力学方程可用于模拟从天文尺度到原子尺度的无数物理系统的时间演化。精确的数值积分需要较小的时间步长，这限制了计算效率——尤其是在像分子动力学这样跨越截然不同时间尺度的情况下。使用机器学习算法预测轨迹可以极大扩展积分时间步长，但代价是引入诸如能量不守恒和系统不同自由度间能量均分丧失等伪影。我们提出学习数据驱动的结构保持（辛且时间可逆）映射来生成长时间步经典动力学，并证明该方法等价于学习目标系统的力学作用量。这些模型可基于短参考轨迹进行学习，并能跨热力学条件和化学组成进行迁移。我们证明，基于作用量的机器学习积分器消除了非结构保持机器学习预测器的病态行为，且该方法可迭代应用，作为对计算成本更低的直接预测器的校正。