Markov chain Monte Carlo with neural network surrogates: application to contaminant source identification
- PDF / 2,161,560 Bytes
- 13 Pages / 595.276 x 790.866 pts Page_size
- 99 Downloads / 216 Views
ORIGINAL PAPER
Markov chain Monte Carlo with neural network surrogates: application to contaminant source identification Zitong Zhou1 • Daniel M. Tartakovsky1 Accepted: 26 September 2020 Ó Springer-Verlag GmbH Germany, part of Springer Nature 2020
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 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. Keywords MCMC CNN Surrogate model Source identification
1 Introduction Identification of contaminant release history in groundwater plays an important role in regulatory efforts and design of remedial actions. Such efforts rely on measurements of solute concentrations collected at a few locations (pumping or observation wells) in an aquifer. Data collection can take place at discrete times and is often plagued by measurement errors. A release history is estimated by matching these data to predictions of a solute transport model, an inverse modeling procedure that is typically ill-posed. Alternative strategies for solving this inverse problem (Amirabdollahian and Datta 2013; Zhou et al. 2014; Rajabi et al. 2018; Barajas-Solano et al. 2019) fall into two categories: deterministic and probabilistic. Deterministic methods include least squares regression (White 2015) and hybrid optimization with a genetic algorithm (Ayvaz 2016; Leichombam and Bhattacharjya 2018). They provide a & Daniel M. Tartakovsky [email protected] 1
Department of Energy Resources Engineering, Stanford University, Stanford, CA, USA
‘‘best’’ estimate of the contaminant release history, without quantifying the uncertainty inevitable in such predictions. Probabilistic methods, e.g., data assimilation via extended and ensemble Kalman filters (Xu and Go´mez-Herna´ndez 2016, 2018) and Bayesian inference based on Markov chain Monte Carlo or MCMC (Gamerman and Lopes 2006), overcome this shortcoming. Kalman filters are relatively fast but do not generalize to strongly nonlinear problems, sometimes exhibiting inconsistency between updated parameters and
Data Loading...
