Gaussian Process Regression for Maximum Entropy Distribution
Mohsen Sadr Manuel Torrilhon M. Hossein Gorji
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.