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 reduce 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.

中文翻译：

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带有神经网络代理的马尔可夫链蒙特卡罗：在污染源识别中的应用

地下修复通常涉及从溶质浓度的稀疏观察中重建污染物释放历史。马尔可夫链蒙特卡罗 (MCMC) 是完成这项任务的最准确和通用的方法，但在实践中很少使用，因为它与污染物传输方程的多次求解相关的计算成本很高。我们提出了一种自适应 MCMC 方法，其中传输模型被一个快速准确的替代模型所取代，该模型以深度卷积神经网络 (CNN) 的形式出现。基于未知发布历史的先验知识，对基于 CNN 的代理进行了少量传输模型运行的训练。因此，减少的计算成本允许减少与构造近似似然函数相关的采样误差。与所有用于源识别的 MCMC 策略一样，我们的方法具有量化预测不确定性和解释测量误差的额外优势。我们的数值实验证明了与具有前向传输模型的 MCMC 相媲美的精度，其计算成本仅为后者的一小部分。