Physics-constrained, data-driven discovery of coarse-grained dynamics
This addresses the challenge of developing accurate coarse-grained models for computational physics, offering a probabilistic approach that handles information loss, but it is incremental as it builds on existing coarse-graining and sparse Bayesian methods.
The paper tackles the problem of coarse-graining high-dimensional systems with disparate time scales by proposing a data-driven, physics-constrained method to discover governing equations from fine-scale simulation data, resulting in a framework that quantifies predictive uncertainty and reconstructs fine-scale evolution, as demonstrated in systems of random walkers.
The combination of high-dimensionality and disparity of time scales encountered in many problems in computational physics has motivated the development of coarse-grained (CG) models. In this paper, we advocate the paradigm of data-driven discovery for extract- ing governing equations by employing fine-scale simulation data. In particular, we cast the coarse-graining process under a probabilistic state-space model where the transition law dic- tates the evolution of the CG state variables and the emission law the coarse-to-fine map. The directed probabilistic graphical model implied, suggests that given values for the fine- grained (FG) variables, probabilistic inference tools must be employed to identify the cor- responding values for the CG states and to that end, we employ Stochastic Variational In- ference. We advocate a sparse Bayesian learning perspective which avoids overfitting and reveals the most salient features in the CG evolution law. The formulation adopted enables the quantification of a crucial, and often neglected, component in the CG process, i.e. the pre- dictive uncertainty due to information loss. Furthermore, it is capable of reconstructing the evolution of the full, fine-scale system. We demonstrate the efficacy of the proposed frame- work in high-dimensional systems of random walkers.