An adaptive Gaussian process‐based method for efficient Bayesian experimental design in groundwater contaminant source identification problems

Surrogate models are commonly used in Bayesian approaches such as Markov Chain Monte Carlo (MCMC) to avoid repetitive CPU‐demanding model evaluations. However, the approximation error of a surrogate may lead to biased estimation of the posterior distribution. This bias can be corrected by constructing a very accurate surrogate or implementing MCMC in a two‐stage manner. Since the two‐stage MCMC requires extra original model evaluations after surrogate evaluations, the computational cost is still high. If the information of measurement is incorporated, a locally accurate surrogate can be adaptively constructed with low computational cost. Based on this idea, we integrate Gaussian process (GP) and MCMC to adaptively construct locally accurate surrogates for Bayesian experimental design in groundwater contaminant source identification problems. Moreover, the uncertainty estimate of GP approximation error is incorporated in the Bayesian formula to avoid over‐confident estimation of the posterior distribution. The proposed approach is tested with a numerical case study. Without sacrificing the estimation accuracy, the new approach achieves about 200 times of speed‐up compared to our previous work which implemented MCMC in a two‐stage manner. Key Points: A locally accurate surrogate is adaptively constructed with Gaussian process The approximation error of the surrogate is rigorously considered Surrogate‐based experimental design and inversion are applied to identify contaminant source