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.
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页数：15
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