# Gaussian Process Regression for Maximum Entropy Distribution

**Authors:** Mohsen Sadr, Manuel Torrilhon, M. Hossein Gorji  
**arXiv:** [2308.06149](https://arxiv.org/abs/2308.06149)  
**Date:** 2023-08-11  
**Summary page:** https://www.summarizepaper.com/fr/arxiv-id/2308.06149v1/

## 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.