Subsurface remediation often involves reconstruction of contaminant release history from sparse observations of solute concentration. Markov Chain Monte Carlo (MCMC), the most accurate and general method for this task, is rarely used in practice because of its high computational cost associated with multiple solves of contaminant transport equations. We propose an adaptive MCMC method, in which a transport model is replaced with a fast and accurate surrogate model in the form of a deep convolutional neural network (CNN). The CNN-based surrogate is trained on a small number of the transport model runs based on the prior knowledge of the unknown release history. Thus reduced computational cost allows one to diminish the sampling error associated with construction of the approximate likelihood function. As all MCMC strategies for source identification, our method has an added advantage of quantifying predictive uncertainty and accounting for measurement errors. Our numerical experiments demonstrate the accuracy comparable to that of MCMC with the forward transport model, which is obtained at a fraction of the computational cost of the latter.

地下修复通常涉及从稀疏的溶质浓度观测值重建污染物释放历史。马尔可夫链蒙特卡洛（MCMC）是用于此任务的最准确，最通用的方法，由于其与污染物迁移方程的多次求解相关的高计算成本，因此在实践中很少使用。我们提出了一种自适应MCMC方法，其中以深度卷积神经网络（CNN）的形式用快速，准确的替代模型代替运输模型。基于CNN的代理基于未知发布历史的先验知识在少量运输模型运行中进行训练。因此，降低的计算成本允许人们减少与近似似然函数的构造相关的采样误差。作为所有用于源识别的MCMC策略，我们的方法还具有量化预测不确定性和考虑测量误差的附加优势。我们的数值实验表明，与前向传输模型相比，其精度可与MCMC媲美，而前向传输模型的计算成本仅为后者的一小部分。