Volume 25, Issue 5
Physics-Constrained, Data-Driven Discovery of Coarse-Grained Dynamics

Lukas Felsberger & Phaedon-Stelios Koutsourelakis

Commun. Comput. Phys., 25 (2019), pp. 1259-1301.

Published online: 2019-01

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  • Abstract

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.

  • Keywords

Coarse-graining, dynamics, Bayesian, non-equilibrium, data-driven.

  • AMS Subject Headings

62F15, 82C21, 82C80

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-25-1259, author = {}, title = {Physics-Constrained, Data-Driven Discovery of Coarse-Grained Dynamics}, journal = {Communications in Computational Physics}, year = {2019}, volume = {25}, number = {5}, pages = {1259--1301}, abstract = {

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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2018-0174}, url = {http://global-sci.org/intro/article_detail/cicp/12951.html} }
TY - JOUR T1 - Physics-Constrained, Data-Driven Discovery of Coarse-Grained Dynamics 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 -

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.

Lukas Felsberger & Phaedon-Stelios Koutsourelakis. (2020). Physics-Constrained, Data-Driven Discovery of Coarse-Grained Dynamics. Communications in Computational Physics. 25 (5). 1259-1301. doi:10.4208/cicp.OA-2018-0174
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