{
  "id": "2308.06149",
  "version": "v1",
  "published": "2023-08-11T14:26:29.000Z",
  "updated": "2023-08-11T14:26:29.000Z",
  "title": "Gaussian Process Regression for Maximum Entropy Distribution",
  "authors": [
    "Mohsen Sadr",
    "Manuel Torrilhon",
    "M. Hossein Gorji"
  ],
  "journal": "Journal of Computational Physics, Volume 418, 2020, 109644",
  "doi": "10.1016/j.jcp.2020.109644",
  "categories": [
    "stat.ML",
    "cs.LG",
    "math-ph",
    "math.MP",
    "physics.data-an"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-11T14:26:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gaussian process regression",
      "maximum entropy distribution",
      "lagrange multipliers",
      "moment closure problems",
      "maximum-entropy distributions offer"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}