We introduced a novel method to solve Bayesian inverse problems governed by PDE equations with a hybrid two-level MCMC where we took advantage of the AI surrogate model speed and the accuracy of numerical models. We show theoretically the potential to solve Bayesian inverse problems accurately with only a small number of numerical samples when the AI surrogate model error is small. Several numerical experiment results are included which demonstrates the advantage of the hybrid method.

翻译：我们提出了一种求解偏微分方程约束贝叶斯反问题的新型方法——混合双层马尔可夫链蒙特卡洛（Hybrid Two-Level MCMC）。该方法融合了人工智能代理模型的计算速度优势与数值模型的精度特征。理论分析表明，在AI代理模型误差较小的情况下，仅需少量数值样本即可实现贝叶斯反问题的精确求解。文中包含多组数值实验结果，充分验证了该混合方法的优越性。