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.

最大熵分布提供了一个有吸引力的概率密度系列，适用于力矩闭合问题。然而，找到对这些分布进行参数化的拉格朗日乘数，事实证明这是实际闭合设置的计算瓶颈。受最近高斯过程成功的推动，我们研究了高斯先验将拉格朗日乘数近似为给定时刻映射的适用性。检查各种内核功能，通过最大化对数似然来优化超参数。在几个测试案例中研究了设计的数据驱动的最大熵闭包的性能，其中包括放宽由Bhatnagar-Gross-Krook和Boltzmann动力学方程控制的非平衡分布。