Gaussian Process Regression for Maximum Entropy Distribution

被引：12

作者：

Sadr, Mohsen ^{[1
]}

Torrilhon, Manuel ^{[1
]}

Gorji, M. Hossein ^{[2
]}

机构：

[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

来源：

JOURNAL OF COMPUTATIONAL PHYSICS | 2020年 / 418卷

基金：

瑞士国家科学基金会;

关键词：

Gaussian process regression; Maximum entropy distribution; Moment problem; MOMENT CLOSURES; CONVERGENCE CONDITIONS; ALGORITHM; DENSITY;

D O I：

10.1016/j.jcp.2020.109644

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

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.

引用

页数：15

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