Macroscopic observables of a system are of keen interest in real applications such as the design of novel materials. Current methods rely on microscopic trajectory simulations, where the forces on all microscopic coordinates need to be computed or measured. However, this can be computationally prohibitive for realistic systems. In this paper, we propose a method to learn macroscopic dynamics requiring only force computations on a subset of the microscopic coordinates. Our method relies on a sparsity assumption: the force on each microscopic coordinate relies only on a small number of other coordinates. The main idea of our approach is to map the training procedure on the macroscopic coordinates back to the microscopic coordinates, on which partial force computations can be used as stochastic estimation to update model parameters. We provide a theoretical justification of this under suitable conditions. We demonstrate the accuracy, force computation efficiency, and robustness of our method on learning macroscopic closure models from a variety of microscopic systems, including those modeled by partial differential equations or molecular dynamics simulations.

本研究解决了宏观可观测量依赖于复杂微观轨迹模拟计算的难题，提出了一种只需在部分微观坐标上计算力的新方法。通过假设微观坐标间的稀疏性，我们的方法高效地将训练过程从宏观坐标映射回微观坐标，显著提高了计算效率和准确性，展现了对多种微观系统的适应性。

从部分微观观察中学习宏观动力学