论文标题
Markov Chain蒙特卡洛（Monte Carlo）具有神经网络代理：应用于污染物来源识别
Markov Chain Monte Carlo with Neural Network Surrogates: Application to Contaminant Source Identification
论文作者
论文摘要
地下修复通常涉及从稀疏溶质浓度的稀疏观察结果中重建污染物释放的历史。马尔可夫链蒙特卡洛（MCMC）是该任务最准确，最通用的方法，在实践中很少使用，因为它与多个污染物传输方程相关的高计算成本。我们提出了一种自适应MCMC方法，其中以深层卷积神经网络（CNN）形式将传输模型替换为快速准确的替代模型。基于CNN的替代物经过少量运输模型的培训，该模型根据未知发行历史的先验知识进行了培训。因此，降低的计算成本使人们可以减少与构建近似似然函数相关的采样误差。作为所有MCMC来源识别策略，我们的方法具有量化预测不确定性和计算错误的额外优势。我们的数值实验证明了与向前传输模型相当的准确性，该准确性是在后者的计算成本的一部分中获得的。
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.
