Gaussian Process Regression for Maximum Entropy Distribution

• URL: http://arxiv.org/abs/2308.06149v1
• Date: Fri, 11 Aug 2023 14:26:29 GMT
• Title: Gaussian Process Regression for Maximum Entropy Distribution
• Authors: Mohsen Sadr, Manuel Torrilhon, M. Hossein Gorji
• Abstract summary: We investigate the suitability of Gaussian priors to approximate the Lagrange multipliers as a map of a given set of moments. The performance of the devised data-driven Maximum-Entropy closure is studied for couple of test cases.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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.

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