Bayesian set pair analysis and machine learning based ensemble surrogates for optimal multi-aquifer system remediation design

Surrogate models are often adopted to substitute computationally intensive groundwater simulation models for aquifer management due to their high effectiveness and computing efficiency. However, solutions of using only one surrogate model are prone to large prediction uncertainty. This study compares individual surrogate models and an ensemble surrogate model in an optimal groundwater remediation design problem. Three machine learning based surrogate models (response surface regression model, artificial neural network and support vector machine) were developed to replace a high-fidelity solute transport model for predicting saltwater intrusion and assisting saltwater scavenging design. An optimal Latin hypercube design was employed to generate training and testing datasets. Set pair analysis was employed to construct a more reliable ensemble surrogate and to address prediction uncertainty arising from individual surrogate models. Bayesian set pair weights were derived by utilizing full information from both training and testing data and improved typical set pair weights. The individual and ensemble surrogate models were applied to the salinization remediation problem in the Baton Rouge area, southeast Louisiana. The optimal remediation design includes two conflicting objectives: minimizing total groundwater extraction from a horizontal scavenger well while maximizing chloride concentration difference to the MCL (maximum contamination level) at monitoring locations. NSGA-II (Non-dominated Sorting Genetic Algorithm II) was employed to solve the nonlinear optimization model and obtain Pareto-optimal pumping schedules. The optimal pumping schedules from ensemble surrogate models and individual surrogate models were verified by the solute transport model. The study found that Bayesian set pair analysis builds robust ensemble surrogates and accounts for model prediction uncertainty. The ensemble-surrogate-assisted optimization model provides stable and reliable solutions while considerably alleviating computational burden.