Gaussian Processes with Functional Inputs with Applications to the Water Erosion Prediction Project Computer Model
The USDA’s Water Erosion Prediction Project (WEPP) computer model utilizes weather, watershed topography, soil type, and land use to estimate water runoff, soil movement, and soil loss. We are constructing Gaussian Process (GP) emulators of this computer model to enable calibration, optimal design, and as a surrogate for WEPP itself. The inputs to this model include a variety of functionals: slope (or elevation) as a function of distance, soil characteristics as function of distance and depth, and precipitation as a function of time. Building a GP emulator requires distances for each of these different types of functions. We build a weighted L2-norm for slope and, incorporated into a GP, we refer to this approach as Automatic Dynamic Relevance Determination. We compare several forms of weight functions including asymmetric Gaussian and Laplace functions as well as B-splines. We observed similar out-of-sample predictive performance amongst all these methods and improvement over Automatic Relevance Determination. Utilizing Bayesian inference, we additionally obtain uncertainty over the weight functions that provide insight into the mechanistic process driving soil loss.