Gaussian Process Regression Approach for modeling subsurface flow

Inverse modeling involves repeated evaluations of the forward simulation, which can be computationally prohibitive for large numerical models. To reduce the overall computational burden of these simulations, we study the use of Gaussian process (GP) regression models as numerical surrogates. Similar to most reduced order models (ROMs), GP regression models involve using solutions at different sample points within the parameter space to construct an approximate solution at any point within the parameter space. However, since GP regression models are derived from a statistical Bayesian framework, they provide valuable statistical insights that can be incorporated into parameter estimation and uncertainty quantification algorithms. More importantly, we show that the resulting ROMs perform better than look-up tables, particularly when the number of sample points is small. We also show how these sample points can be optimally chosen to minimize computational efforts without user intervention. The GP regression models are currently implemented as part of a family of ROMs within the inverse modeling framework of iTOUGH2. We will demonstrate how GP regression models can be used within the iTOUGH2 framework to improve performance of uncertainty quantification.