Learning Macroscopic Dynamics from Partial Microscopic Observations
This addresses a computational bottleneck for researchers and engineers in fields like materials science, where simulating macroscopic observables is prohibitive, though it is incremental as it builds on existing methods with a sparsity assumption.
The paper tackles the problem of learning macroscopic dynamics from microscopic systems, which is computationally expensive due to requiring force computations on all microscopic coordinates. The result is a method that uses only partial force computations, achieving accuracy and efficiency in learning macroscopic closure models from systems like partial differential equations or molecular dynamics simulations.
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.