A review of surrogate models and their application to groundwater modeling

The spatially and temporally variable parameters and inputs to complex groundwater models typically result in long runtimes which hinder comprehensive calibration, sensitivity, and uncertainty analysis. Surrogate modeling aims to provide a simpler, and hence faster, model which emulates the specified output of a more complex model in function of its inputs and parameters. In this review paper, we summarize surrogate modeling techniques in three categories: data-driven, projection, and hierarchical-based approaches. Data-driven surrogates approximate a groundwater model through an empirical model that captures the input-output mapping of the original model. Projection-based models reduce the dimensionality of the parameter space by projecting the governing equations onto a basis of orthonormal vectors. In hierarchical or multifidelity methods the surrogate is created by simplifying the representation of the physical system, such as by ignoring certain processes, or reducing the numerical resolution. In discussing the application to groundwater modeling of these methods, we note several imbalances in the existing literature: a large body of work on data-driven approaches seemingly ignores major drawbacks to the methods; only a fraction of the literature focuses on creating surrogates to reproduce outputs of fully distributed groundwater models, despite these being ubiquitous in practice; and a number of the more advanced surrogate modeling methods are yet to be fully applied in a groundwater modeling context.