Contaminant source localization via Bayesian global optimization

Abstract

Abstract. A Bayesian optimization approach to localize a contaminant source is proposed. The localization problem is illustrated with two 2D synthetic cases which display sharp transmissivity contrasts and specific connectivity patterns. These cases generate highly non-linear 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 minimum of the objective function which identifies the contaminant source. In addition, the generated objective functions 5 are made available as a benchmark to further allow the comparison of optimization algorithms on functions characterized by multiple minima and inspired by concrete field applications.

r2ogs5: Calibration of Numerical Groundwater Flow Models with Bayesian Optimization in R

“…When applying gradient‐based methods in conjunction with multi‐start sampling algorithms in order to increase the probability of finding the global optimum, the number of total required NGWM runs is further multiplied (Gorelick and Zheng 2015). Similarly, probabilistic approaches such as simulated annealing (SA) require hundreds of model runs and are not suitable for computationally expensive NGWM such as regional‐scale models (Pirot et al 2019).…”

“…In geoscience, however, there are only a few studies reporting the use of BO (Hamdi et al 2017; Christelis et al 2019; Pirot et al 2019). Other sophisticated surrogate based optimization algorithms, named “adaptive‐recursive approach” by Razavi et al 2012, follow a similar logic as BO and are popular for solving design problems in the environmental sciences (Bau and Mayer 2006; Di Pierro et al 2009; Fen et al 2009).…”

Using global Bayesian optimization in ensemble data assimilation: parameter estimation, tuning localization and inflation, or all of the above

“…Optimization problems with the above two characteristics occur frequently in the Earth sciences and it is natural to ask if and how one may be able to use GBO in Earth science problems. An example of the use of GBO in a geophysical problem is the recent work of Pirot et al (2019), where GBO is used for underground contaminant source localization. A second example is the work of Abbas et al (2016), which leverages GBO in the context of simultaneous state and parameter estimation problems.…”

Advanced techniques for solving groundwater and surface water problems in the context of inverse methods and climate change.

“…The first category includes the Tikhonov regularization (Skaggs & Kabala 1994), nonlinear optimization with embedding (Mahar & Datta 1997), non-regularized nonlinear least squares (Alapati & Kabala 2000), progressive genetic algorithms (Aral et al 2001), a constrained robust least squares (Sun et al 2006) and heuristic harmony search algorithms (Ayvaz 2010). The second category adopts probability-based methods: statistical pattern recognition (Datta et al 1989); minimum relative entropy (Woodbury & Ulrych 1996, Woodbury et al 1998; geostatistical approaches (Snodgrass & Kitanidis 1997, Michalak & Kitanidis 2004a,b, Neupauer et al 2000, Butera & Tanda 2003, Butera et al 2006, Gzyl et al 2014; empirical Bayesian methods combined with Akaike's Bayesian Information Criterion (Zanini & Woodbury 2016); Bayesian global optimization (Pirot et al 2019) and ensemble Kalman filter methods (Xu & Gómez-Hernández 2016, 2018, Chen et al 2018, Xu et al 2020).…”