Multi-objective Optimization for Island Groundwater Management: Efficient Training of Gaussian Process Models

Coastal groundwater management serves as a widely adopted approach to strike a balance between controlling seawater intrusion (SWI) and meeting local water demands. However, the management objectives and constraints are inevitably conflicting, and this challenge can be addressed through the integration of optimization algorithms and computationally intensive groundwater flow simulators. These simulators, although accurate, often demand significant computational resources. To save computing time, data-driven surrogate models, are employed to replace groundwater flow simulators to immediately estimate aquifer response given the pumping pattern during optimization, which stem from the original simulators using a set of training points and balance the dual requirements of accuracy and computational efficiency. The selection of training samples is pivotal to this process, ensuring the desired accuracy while ensuring computational efficiency. Therefore, this study explores efficient strategies for offline and online training surrogate models in the context of multi-objective coastal groundwater management. Our results indicate that the iterative search algorithm choosing sampling points based on the distance to training points and gradients is suitable for offline-trained surrogate models, while the algorithm that discretizes the Pareto-optimal objective space and chooses points near each subregion center as new training points is appropriate for online-trained surrogate models. The pros and cons of using offline and online-trained surrogate models in the context of coastal groundwater management are analyzed and emphasized.