Contaminant source localization via Bayesian global optimization

Abstract

Contaminant source localization problems require efficient and robust methods that can account for geological heterogeneities and accommodate relatively small data sets of noisy observations. As realism commands hi-fidelity simulations, computation costs call for global optimization algorithms under parsimonious evaluation budgets. Bayesian optimization approaches are well adapted to such settings as they allow the exploration of parameter spaces in a principled way so as to iteratively locate the point(s) of global optimum while maintaining an approximation of the objective function with an instrumental quantification of prediction uncertainty. Here, we adapt a Bayesian optimization approach to localize a contaminant source in a discretized spatial domain. We thus demonstrate the potential of such a method for hydrogeological applications and also provide test cases for the optimization community. The localization problem is illustrated for cases where the geology is assumed to be perfectly known. Two 2-D synthetic cases that display sharp hydraulic conductivity contrasts and specific connectivity patterns are investigated. These cases generate highly nonlinear objective functions that present multiple local minima. A derivative-free global optimization algorithm relying on a Gaussian process model and on the expected improvement criterion is used to efficiently localize the point of minimum of the objective functions, which corresponds to the contaminant source location. Even though concentration measurements contain a significant level of proportional noise, the algorithm efficiently localizes the contaminant source location. The variations of the objective function are essentially driven by the geology, followed by the design of the monitoring well network. The data and scripts used to generate objective functions are shared to favor reproducible research. This contribution is important because the functions present multiple local minima and are inspired from a practical field application. Sharing these complex objective functions provides a source of test cases for global optimization benchmarks and should help with designing new and efficient methods to solve this type of problem.

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