Bayesian probabilistic numerical methods for numerical integration offer
significant advantages over their non-Bayesian counterparts: they can encode
prior information about the integrand, and can quantify uncertainty over
estimates of an integral. However, the most popular algorithm in this class,
Bayesian quadrature, is based on Gaussian process models and is therefore
associated with a high computational cost. To improve scalability, we propose
an alternative approach based on Bayesian neural networks which we call
Bayesian Stein networks. The key ingredients are a neural network architecture
based on Stein operators, and an approximation of the Bayesian posterior based
on the Laplace approximation. We show that this leads to orders of magnitude
speed-ups on the popular Genz functions benchmark, and on challenging problems
arising in the Bayesian analysis of dynamical systems, and the prediction of
energy production for a large-scale wind farm.

本文介绍了一种基于 Stein 运算符的神经网络架构和 Laplace 近似的贝叶斯斯坦网络方法，以实现数值积分中的贝叶斯概率数值方法，相较于高成本的高斯过程模型，该方法在流体力学中的应用中表现了数倍的性能提高。