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\begin{document}

\title{Markov Chain Monte Carlo with Neural Network Surrogates: Application to
Contaminant Source Identification}



\author[1]{Zitong Zhou}%
\author[1]{Daniel M Tartakovsky}%
\affil[1]{Stanford University}%


\vspace{-1em}



  
  \date{May 24, 2024}


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\begin{abstract}
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.%
\end{abstract}%



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