Gaussian Process Regression for Maximum Entropy Distribution
Abstract
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.
Cite
@article{arxiv.2308.06149,
title = {Gaussian Process Regression for Maximum Entropy Distribution},
author = {Mohsen Sadr and Manuel Torrilhon and M. Hossein Gorji},
journal= {arXiv preprint arXiv:2308.06149},
year = {2023}
}