Multi-Fidelity Surrogates of Groundwater Flow

Abstract:

In order to support decision making under uncertainty, models must provide detailed predictions in a timely manner. While highly parametrized models allow a gamut of data and processes to be incorporated at fine temporal and spatial scales, their slow runtimes inhibit their use in optimization, uncertainty analysis, integrated modelling, and decision support. Surrogate modelling attempts to reproduce the relevant behaviour of a complex mode, at a fraction of the computational cost. Data-driven surrogate methods (e.g. Radial Basis Functions) have shown promise in replicating a relatively small number of input-output relationships. However, they are not suited to models with hundreds of inputs or outputs. Other drawbacks of data-driven methods include poor performance away from runs used to calibrate the surrogate. Hierarchical (e.g. Multigrid) and Projection (e.g. Proper Orthogonal Decomposition) based surrogates are less prone to these drawbacks. Novel methods, such as multi-fidelity stochastic collocation, combine techniques from both Hierarchical and Projection based methods. In this work, we apply such an approach to a transient, spatially distributed groundwater flow model. While the surrogate runtime is orders of magnitude lower than the original model, it reproduces the hundreds of values necessary to characterize spatially and temporally varying outputs. The surrogate allows uncertainty in aquifer properties to be propagated to head time-series at a number of locations.