Environmental Modeling Framework using Stacked Gaussian Processes

A network of independently trained Gaussian processes (StackedGP) is introduced to obtain predictions of quantities of interest with quantified uncertainties. The main applications of the StackedGP framework are to integrate different datasets through model composition, enhance predictions of quantities of interest through a cascade of intermediate predictions, and to propagate uncertainties through emulated dynamical systems driven by uncertain forcing variables. By using analytical first and second-order moments of a Gaussian process with uncertain inputs using squared exponential and polynomial kernels, approximated expectations of quantities of interests that require an arbitrary composition of functions can be obtained. The StackedGP model is extended to any number of layers and nodes per layer, and it provides flexibility in kernel selection for the input nodes. The proposed nonparametric stacked model is validated using synthetic datasets, and its performance in model composition and cascading predictions is measured in two applications using real data.