This paper focuses on accelerating Markov chain Monte Carlo sampling in Bayesian inverse problems in which forward model evaluations dominate the computational cost. It builds on several established ingredients previously used in related scenarios: delayed acceptance, neural network surrogate models, Hamiltonian proposals, and proposal subchains. The main framework is the delayed-acceptance Metropolis-Hastings algorithm of Christen and Fox (2005). The first-stage proposal distribution is constructed from a subchain of Hamiltonian trajectories targeting the surrogate posterior. For each fixed surrogate model, the Hamiltonian subchain and delayed-acceptance correction define a kernel invariant with respect to the exact posterior. In the present work, the surrogate is updated only during a burn-in phase, after which the production run uses a fixed surrogate model. The sampling framework is implemented in Python using parallel processes. Several chains are generated in parallel and share a single surrogate model trained during burn-in on all collected data. The forward model is treated as a black box; therefore, the application area is broad. However, the main motivation is efficient solution of geotechnical inverse problems with material properties represented by Gaussian random fields. In this study, the sampling framework is applied to a geotechnical inverse problem in which hydraulic conductivity and porosity are modeled as non-stationary Gaussian random fields approximated using truncated Karhunen-Loeve expansions. Based on a precomputation, the truncation dimensions are chosen separately for hydraulic conductivity and porosity. The forward model outputs are pore pressure values at control points and selected observation times. These are compared with in situ pore pressure measurements collected over one year during the Tunnel Sealing Experiment in an underground laboratory in Canada.

翻译：[translated abstract in Chinese] 本文聚焦于加速贝叶斯反问题中的马尔可夫链蒙特卡洛采样，其中正演模型评估主导了计算成本。该方法建立在先前相关场景中使用的若干成熟要素之上：延迟接受、神经网络代理模型、哈密顿提议及提议子链。主要框架基于Christen与Fox (2005)提出的延迟接受Metropolis-Hastings算法。第一阶段的提议分布由指向代理后验的哈密顿轨迹子链构建而成。对于每个固定代理模型，哈密顿子链与延迟接受校正定义了一个关于精确后验保持不变的核。本工作中，代理仅在预热阶段更新，生产运行阶段则使用固定的代理模型。采样框架采用Python并行进程实现。多条链并行生成，共享一个在预热阶段基于所有收集数据训练的代理模型。正演模型被视为黑箱，因此该方法具有广泛适用性。然而，其主要动机在于高效求解以高斯随机场表征材料特性的岩土工程反问题。本研究将采样框架应用于岩土工程反问题，其中水力传导率和孔隙度通过截断Karhunen-Loeve展开近似为非平稳高斯随机场。基于预计算，水力传导率与孔隙度的截断维度分别选取。正演模型输出为控制点处孔隙压力值及选定观测时刻的数据。这些结果与加拿大某地下实验室"隧道密封实验"中一年期间采集的原位孔隙压力测量值进行对比。