论文标题
基于本地Karhunen-Loève扩展，域被构成的贝叶斯反演
Domain-decomposed Bayesian inversion based on local Karhunen-Loève expansions
论文作者
论文摘要
在许多贝叶斯反问题中，目标是恢复空间变化的随机场。这些问题通常在计算上具有挑战性，尤其是当正向模型受复杂的部分微分方程（PDE）约束时。当空间结构域很大并且需要由高维参数表示未知的随机场时，挑战尤其严重。在本文中，我们提出了一种域被计算的方法，用于攻击维度问题，该方法同时分解了空间域和参数域。在每个子域中，构建了局部的karhunen-lo` eve（KL）扩展，并以平行方式独立解决局部反转问题，更重要的是在较低维的空间中。通过对亚域进行马尔可夫链蒙特卡洛（MCMC）模拟产生局部后样品后，开发了一种新的投影程序来有效地重建全球场。此外，域分解界面条件与基于自适应的高斯拟合策略有关。提供了数值示例以证明所提出的方法的性能。
In many Bayesian inverse problems the goal is to recover a spatially varying random field. Such problems are often computationally challenging especially when the forward model is governed by complex partial differential equations (PDEs). The challenge is particularly severe when the spatial domain is large and the unknown random field needs to be represented by a high-dimensional parameter. In this paper, we present a domain-decomposed method to attack the dimensionality issue and the method decomposes the spatial domain and the parameter domain simultaneously. On each subdomain, a local Karhunen-Lo`eve (KL) expansion is constructed, and a local inversion problem is solved independently in a parallel manner, and more importantly, in a lower-dimensional space. After local posterior samples are generated through conducting Markov chain Monte Carlo (MCMC) simulations on subdomains, a novel projection procedure is developed to effectively reconstruct the global field. In addition, the domain decomposition interface conditions are dealt with an adaptive Gaussian process-based fitting strategy. Numerical examples are provided to demonstrate the performance of the proposed method.
