Comparison of off-line and on-line trained Gaussian process models for island groundwater management

 In coastal groundwater management, surrogate-modelling techniques are often used to substitute complex numerical simulation models to identify optimal pumping strategies that limit seawater intrusion. The performance of a surrogate model highly depends on the training information provided by the original simulation model, so a crucial issue is to determine an adequate sampling size to strike a balance between surrogate model accuracy and computing efficiency. Since the optimal sampling size usually differs depending on the choices of function approximation techniques, training framework, sampling method and the complexity of the management problem, there are currently no general and systematic conclusions concerning the optimal sampling size. This work proposes general guidelines for choosing a suitable strategy to develop surrogate models for the management of groundwater resources in island aquifers. These are established in accordance with the dimension of the management problem, including the training framework (off-line vs. on-line), discretization scheme over the entire input space and a reasonable sample size. This work considers, as a case study, a simplified conceptual model (Figure 1) of the San Salvador Island (Bahamas), and adopts a Gaussian process (GP) and a Latin hypercube sampling method to build surrogate functions representing the groundwater supply operation cost and the intensity of seawater intrusion and depending on up to three decision variables. Decision variables include the distance of a well system to the shoreline (WL), the pumping depth (D) and the total groundwater-pumping rate (Q). This approach leads to identifying the surrogate training samples needed to build reliable GP models using both off-line and online frameworks, and allows for their direct comparison in terms of model robustness and computing efficiency. 

Oral Presentation at:  American Geophysical Union's 2022 Frontiers in Hydrology Meeting Conference, San Juan, Puerto Rico, 19-24 June 2022