  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.
