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.

翻译：最大熵分布为矩封闭问题提供了一类吸引人的概率密度函数族。然而，寻找参数化这些分布的拉格朗日乘子，在实际封闭设置中成为计算瓶颈。受高斯过程近期成功的启发，我们研究了利用高斯先验近似拉格朗日乘子（作为给定矩集合的映射）的适用性。通过检验多种核函数，并最大化对数似然来优化超参数。我们针对若干测试案例，包括由Bhatnagar-Gross-Krook和Boltzmann动力学方程控制的非平衡分布松弛过程，对所提出的数据驱动最大熵封闭方法的性能进行了研究。