Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Physics-constrained, data-driven discovery of coarse-grained dynamics   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.

12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
2
The categories of this paper are: math
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph