标题： 插值误差和偏差对逆问题的随机网格有限元法的影响 显示英文标题

标题： Effects of Interpolation Error and Bias on the Random Mesh Finite Element Method for Inverse Problems

摘要： 贝叶斯反问题是在偏微分方程概率求解器的重要应用之一：当完全解决数值误差在计算上不可行时，概率求解器可用于一致地建模误差并将该误差传播到后验分布。 在这项工作中，我们研究了随机网格有限元方法（RM-FEM）在贝叶斯反问题设置中的性能。 我们展示了插值误差如何对 RM-FEM 后验产生负面影响，并且这些负面影响是如何被减弱的。 在有限元法（FEM）对感兴趣量存在偏差的情况下，我们发现 RM-FEM 难以准确模拟这种偏差。 显示英文摘要

摘要： Bayesian inverse problems are an important application for probabilistic solvers of partial differential equations: when fully resolving numerical error is computationally infeasible, probabilistic solvers can be used to consistently model the error and propagate it to the posterior. In this work, the performance of the random mesh finite element method (RM-FEM) is investigated in a Bayesian inverse setting. We show how interpolation error negatively affects the RM-FEM posterior, and how these negative effects can be diminished. In scenarios where FEM is biased for a quantity of interest, we find that RM-FEM struggles to accurately model this bias.