Scalable Surrogates for Counts and Computer Experiments

Abstract

Data collected by the Interstellar Boundary Explorer (IBEX), recording counts of heliospheric energetic neutral atoms (ENAs), exhibit a phenomenon that has caused space scientists to revise hypotheses about the physical processes, and computer simulations under those models, that are in play at the boundary of our solar system. Providing estimates and associated uncertainty quantification (UQ) of the rate at which ENAs are generated is vital to theory development and validation. Gaussian processes (GPs) constitute an excellent nonparametric regression tool that can provide accurate out-of-sample prediction and UQ. But GPs are unconventional for modeling non-Gaussian observations, are inefficient on large training data, and struggle to model nonstationary response surfaces, all issues present in the IBEX application. To address this gap, I propose a fully Bayesian, Vecchia-approximated, Poisson deep GP surrogate model. I demonstrate its improved predictive capability over competitors through multiple simulated examples. Further, I develop a novel, fully Bayesian framework for solving Bayesian inverse problems, coupling a Poisson response with a Vecchia-approximated GP surrogate of an expensive simulator with high-dimensional output. I demonstrate the utility of this new framework via simulated scenarios in terms of recovering the "true" computer model parameters and enhancing prediction over models that rely exclusively on physical observations. I apply these new technologies to IBEX satellite data and associated computer models developed at Los Alamos National Laboratory.