TY - JOUR
T1 - Physics-Constrained, Data-Driven Discovery of Coarse-Grained Dynamics
AU - Lukas Felsberger & Phaedon-Stelios Koutsourelakis
JO - Communications in Computational Physics
VL - 5
SP - 1259
EP - 1301
PY - 2019
DA - 2019/01
SN - 25
DO - http://doi.org/10.4208/cicp.OA-2018-0174
UR - https://global-sci.org/intro/article_detail/cicp/12951.html
KW - Coarse-graining, dynamics, Bayesian, non-equilibrium, data-driven.
AB - <p style="text-align: justify;">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 extracting 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 dictates 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 corresponding values for the CG states and to that end, we employ Stochastic Variational Inference. 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 predictive 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 framework in high-dimensional systems of random walkers.</p>