Surrogate Groundwater Models

The spatially and temporally variable parameters and inputs to complex groundwater models typically result in long runtimes which hinder comprehensive analysis. These analyses typically involving calibration, sensitivity analysis and uncertainty propagation. Surrogate modelling aims to provide a simpler, and hence faster, model which emulates the specified output of a more complex model as a function of its inputs and parameters. A faster model enables more model runs, critical for understanding models through methods such as sensitivity and uncertainty analysis. Three broad categories of surrogate models are data-driven, projection, and hierarchical-based. 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 basis vectors. In hierarchical or multi-fidelity methods the surrogate is created by simplifying the representation of the physical system, such as by ignoring certain processes, or reducing the numerical resolution. A surrogate method can only be of practical value if it significantly reduces model runtimes, robustly emulates the output and can be implemented simply. A gamut of surrogate techniques have been applied to groundwater and similar partial differential equation based simulators, but the practicability of all approaches is not clear. Among the promising approaches are Polynomial Chaos Expansions (PCE), Multi-fidelity Stochastic Collocation (MFSC) and modern Deep Learning (DL) Neural Networks (NN). These are investigated in the thesis. They represent the three categories above as projection-based (depending on implementation), multi-fidelity and data-driven methods respectively. However all three methods are black box in that they do not require re-implementation of the complex model, making them relevant to practitioners. PCEs are an efficient and statistically rigorous approach with a number of well developed methods for their calibration. In the framework we present, they are suited to accelerating sensitivity analysis and uncertainty propagation of models with a moderate number of parameters. MFSC overcomes many shortcomings of other surrogate methods by employing a lower resolution model as the surrogate. The approach is shown to faithfully emulate spatially and temporally distributed parameters, and allows simply parallelization. While traditional NN are not the most promising surrogate technique, there is potential in the DL software frameworks associated with the recent boom in their popularity. This promise extends not just to efficient uncertainty analysis and data assimilation for groundwater modelling, but numerical modelling in general. Emulation using either PCE, MFSC or DL as demonstrated in this thesis will add value to practical groundwater modelling by not only reducing model runtimes but deepening understanding of the underlying model. The PCE approach iteratively selects the underlying model samples, training a surrogate with less than 1% error in under 200 model runs. The MFSC method achieves similar accuracy with less than 30 full model runs. The DL approaches are less efficient, requiring 500 model runs. However they emulate the full spatially distributed output of the underlying model, and can be applied in situations with 100s of uncertain parameters. Further contributions of this work include two improvements to the MFSC algorithm, reducing surrogate error by two orders of magnitude. We identify a gap between existing research in applied DL, theory-rich applied mathematics and the increasing quantity of spatially distributed data. We create a new surrogate form which combines PCE theory with a DL implementation, and develop another which captures physical aquifer properties during the training of a state of the art DL architecture