标题： 多尺度模型简化方法在地下流Bayesian反问题中的应用 显示英文标题

标题： Multiscale model reduction method for Bayesian inverse problems of subsurface flow

摘要： 本文提出了一种针对地下流动应用中反问题的模型降阶方法。 对于贝叶斯反问题，需要为大量样本重复计算正向模型以获得平稳链，这需要大量的计算工作量。 为了显著提高计算效率，我们使用广义多尺度有限元法和最小二乘随机配置法构建了降阶计算模型。 为了避免选择正则化参数的困难，引入超参数来构建分层模型。 我们使用截断的Karhunen-Loeve展开(KLE)来降低参数空间的维度并减少马尔可夫链的混合时间。 超参数和KLE技术被纳入模型降阶方法中。 降阶模型是在离线阶段构建的。 然后在在线采样阶段高效地进行计算。 该策略可以显著加速马尔可夫链的评估，并且所得后验分布收敛速度快。 我们分析了由降阶模型得到的后验分布与由全阶模型得到的参考后验分布之间的逼近收敛性。 进行了几个地下流动的数值例子，以展示所提出的模型降阶方法在贝叶斯反问题中的性能。 显示英文摘要

摘要： This work presents a model reduction approach to the inverse problem in the application of subsurface flows. For the Bayesian inverse problem, the forward model needs to be repeatedly computed for a large number of samples to get a stationary chain. This requires large computational efforts. To significantly improve the computation efficiency, we use generalized multiscale finite element method and least-squares stochastic collocation method to construct a reduced computational model. To avoid the difficulty of choosing regularization parameter, hyperparameters are introduced to build a hierarchical model. We use truncated Karhunen-Loeve expansion (KLE) to reduce the dimension of the parameter spaces and decrease the mixed time of Markov chains. The techniques of hyperparameter and KLE are incorporated into the model reduction method. The reduced model is constructed offline. Then it is computed very efficiently in the online sampling stage. This strategy can significantly accelerate the evaluation of the Markov chain and the resultant posterior distribution converges fast. We analyze the convergence for the approximation between the posterior distribution by the reduced model and the reference posterior distribution by the full-order model. A few numerical examples in subsurface flows are carried out to demonstrate the performance of the presented model reduction method with application of the Bayesian inverse problem.