Recent advancements in Markov chain Monte Carlo (MCMC) sampling and surrogate modelling have significantly enhanced the feasibility of Bayesian analysis across engineering fields. However, the selection and integration of surrogate models and cutting-edge MCMC algorithms, often depend on ad-hoc decisions. A systematic assessment of their combined influence on analytical accuracy and efficiency is notably lacking. The present work offers a comprehensive comparative study, employing a scalable case study in computational mechanics focused on the inference of spatially varying material parameters, that sheds light on the impact of methodological choices for surrogate modelling and sampling. We show that a priori training of the surrogate model introduces large errors in the posterior estimation even in low to moderate dimensions. We introduce a simple active learning strategy based on the path of the MCMC algorithm that is superior to all a priori trained models, and determine its training data requirements. We demonstrate that the choice of the MCMC algorithm has only a small influence on the amount of training data but no significant influence on the accuracy of the resulting surrogate model. Further, we show that the accuracy of the posterior estimation largely depends on the surrogate model, but not even a tailored surrogate guarantees convergence of the MCMC.Finally, we identify the forward model as the bottleneck in the inference process, not the MCMC algorithm. While related works focus on employing advanced MCMC algorithms, we demonstrate that the training data requirements render the surrogate modelling approach infeasible before the benefits of these gradient-based MCMC algorithms on cheap models can be reaped.

翻译：近年来，马尔可夫链蒙特卡洛（MCMC）采样与代理建模技术的进步，显著提升了贝叶斯分析在工程各领域的可行性。然而，代理模型与前沿MCMC算法的选择与集成通常依赖于临时决策，对其组合如何影响分析精度与效率的系统性评估明显不足。本研究通过一个可扩展的计算力学案例——聚焦于空间变化材料参数的推断——进行了全面的比较分析，揭示了代理建模与采样方法选择的影响。研究表明，即使在低至中等维度下，代理模型的先验训练也会在后验估计中引入较大误差。我们提出了一种基于MCMC算法路径的简单主动学习策略，该策略优于所有先验训练的模型，并确定了其训练数据需求。我们证明，MCMC算法的选择对训练数据量影响较小，且对最终代理模型的精度无显著影响。此外，研究表明后验估计的精度在很大程度上取决于代理模型，但即便是定制的代理模型也无法保证MCMC的收敛性。最后，我们指出前向模型是推断过程中的瓶颈，而非MCMC算法。尽管相关研究侧重于采用先进的MCMC算法，但我们证明，在能够从这些基于梯度的MCMC算法在廉价模型上获益之前，训练数据需求已使得代理建模方法不可行。