# Physics-constrained, data-driven discovery of coarse-grained dynamics

arXiv: https://arxiv.org/abs/1802.03824 · HTML: https://mlsanity.com/paper/1802.03824/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Feb 2018.

## Built on by (most cited first, 3 of 3)

- [Physics-aware, probabilistic model order reduction with guaranteed stability](https://mlsanity.com/paper/2101.05834/) (2021)
- [A probabilistic, data-driven closure model for RANS simulations with aleatoric, model uncertainty](https://mlsanity.com/paper/2307.02432/) (2023)
- [Physics-aware, deep probabilistic modeling of multiscale dynamics in the Small Data regime](https://mlsanity.com/paper/2102.04269/) (2021)

## Abstract (arXiv)

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.