A Review of Surrogate Models and Their Ensembles to Develop Saltwater Intrusion Management Strategies in Coastal Aquifers

The complex physical processes in a typical coastal aquifer system with transient inputs to numerical simulation models (NSM) result in substantial computational burden in a coupled simulation–optimization (S/O) approach. In such situations, an approximate emulator of the complex physical processes provides a computationally efficient alternative to the NSM. The reliability of these surrogate models (SM) within the coupled S/O approach depends on how accurately they capture the trend of the underlying physical processes. Moreover, these SMs are often associated with prediction uncertainties, which hinder optimality of the solution of the coupled S/O methodology. In this review article, we summarize ensemble approach of combining data-driven SMs to address this prediction uncertainty. Different techniques of ensemble formation as well as their relative advantages and disadvantages are also discussed. Although a wide range of data-driven SMs have been used to approximate associated physical processes of coastal aquifers, the use of ensemble SMs is quite limited. Moreover, these ensemble-based modelling approaches are based on manipulating the training data set, i.e., using different realizations of training data set to train individual SMs within the ensemble. Although ensemble formation by combining multiple SMs based on different algorithms can be found in other application domains, the application of ensemble SMs in the prediction of saltwater intrusion processes has not been developed yet. In addition, more advanced ensemble surrogate-modelling approaches are yet to be established in the context of developing regional scale saltwater intrusion management models.