Gaussian Process Regression for Maximum Entropy Distribution

JOURNAL OF COMPUTATIONAL PHYSICS

卷:418

Article

Sadr, Mohsen¹  Torrilhon, Manuel¹  Gorji, M. Hossein² 

[1] Rhein Westfal TH Aachen, Dept Math, MATHCCES, Schinkestr 2, D-52062 Aachen, Germany

[2] Ecole Polytech Fed Lausanne EPFL, MCSS, CH-1015 Lausanne, Switzerland

关键词: Gaussian process regression;    Maximum entropy distribution;    Moment problem;   

DOI  :  10.1016/j.jcp.2020.109644

来源: Elsevier

【 摘 要 】

Maximum-Entropy Distributions offer an attractive family of probability densities suitable for moment closure problems. Yet finding the Lagrange multipliers which parametrize these distributions, turns out to be a computational bottleneck for practical closure settings. Motivated by recent success of Gaussian processes, we investigate the suitability of Gaussian priors to approximate the Lagrange multipliers as a map of a given set of moments. Examining various kernel functions, the hyperparameters are optimized by maximizing the log-likelihood. The performance of the devised data-driven Maximum-Entropy closure is studied for couple of test cases including relaxation of non-equilibrium distributions governed by Bhatnagar-Gross-Krook and Boltzmann kinetic equations. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free