标题： 基于Gevrey正则区域变形的泊松问题受控贝叶斯形状反演的准蒙特卡罗方法 显示英文标题

标题： Quasi-Monte Carlo for Bayesian shape inversion governed by the Poisson problem subject to Gevrey regular domain deformations

摘要： 我们考虑将准蒙特卡洛求积规则应用于在Gevrey正则参数化下的域不确定性条件下，受泊松方程约束的贝叶斯形状反问题。 我们分析了相关后验分布的参数正则性，并设计了随机平移的一阶格子规则，这些规则可以证明能够在后验分布上的高维积分中实现与维度无关、快于蒙特卡洛的求积收敛速度。 此外，我们还考虑了该模型中的维度截断和有限元离散化误差的影响。 最后，给出了一系列数值实验来验证理论结果。 显示英文摘要

摘要： We consider the application of a quasi-Monte Carlo cubature rule to Bayesian shape inversion subject to the Poisson equation under Gevrey regular parameterizations of domain uncertainty. We analyze the parametric regularity of the associated posterior distribution and design randomly shifted rank-1 lattice rules which can be shown to achieve dimension-independent, faster-than-Monte Carlo cubature convergence rates for high-dimensional integrals over the posterior distribution. In addition, we consider the effect of dimension truncation and finite element discretization errors for this model. Finally, a series of numerical experiments are presented to validate the theoretical results.