Multilevel dimension-independent likelihood-informed MCMC for large-scale inverse problems

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS

ACS Applied Bio Materials Pub Date : 2024-02-05 DOI:10.1088/1361-6420/ad1e2c

Tiangang Cui, Gianluca Detommaso, Robert Scheichl

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引用次数: 0

Abstract

We present a non-trivial integration of dimension-independent likelihood-informed (DILI) MCMC (Cui et al 2016) and the multilevel MCMC (Dodwell et al 2015) to explore the hierarchy of posterior distributions. This integration offers several advantages: First, DILI-MCMC employs an intrinsic likelihood-informed subspace (LIS) (Cui et al 2014)—which involves a number of forward and adjoint model simulations—to design accelerated operator-weighted proposals. By exploiting the multilevel structure of the discretised parameters and discretised forward models, we design a Rayleigh–Ritz procedure to significantly reduce the computational effort in building the LIS and operating with DILI proposals. Second, the resulting DILI-MCMC can drastically improve the sampling efficiency of MCMC at each level, and hence reduce the integration error of the multilevel algorithm for fixed CPU time. Numerical results confirm the improved computational efficiency of the multilevel DILI approach.

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用于大规模逆问题的多层次维度独立似然信息 MCMC

我们提出了一种与维度无关的似然信息（DILI）MCMC（Cui 等人，2016 年）和多级 MCMC（Dodwell 等人，2015 年）的非难整合，以探索后验分布的层次结构。这种整合具有几个优势：首先，DILI-MCMC 采用内在似然信息子空间（LIS）（Cui 等人，2014 年）--其中涉及大量前向和邻接模型模拟--来设计加速算子加权建议。通过利用离散参数和离散前向模型的多层次结构，我们设计了一种 Rayleigh-Ritz 程序，以显著减少构建 LIS 和使用 DILI 建议的计算量。其次，由此产生的 DILI-MCMC 可以大幅提高各层次 MCMC 的采样效率，从而在 CPU 时间固定的情况下降低多层次算法的积分误差。数值结果证实了多级 DILI 方法提高了计算效率。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

ACS Applied Bio Materials Chemistry-Chemistry (all)

CiteScore

9.40

自引率

2.10%

发文量

464