Deep Gaussian Process Emulation and Uncertainty Quantification for Large Computer Experiments

TL;DR

This paper introduces a scalable deep Gaussian process framework for emulating complex, non-stationary computer models, with a novel smoothness control parameter and variational inference, demonstrated on astrophysical simulations.

Contribution

It presents a new deep Gaussian process formulation with a smoothness parameter and scalable inference for large computer experiments, addressing non-stationarity.

Findings

Effective emulation of astrophysical models

Scalable to large simulation datasets

Ability to capture non-stationary behaviors

Abstract

Computer models are used as a way to explore complex physical systems. Stationary Gaussian process emulators, with their accompanying uncertainty quantification, are popular surrogates for computer models. However, many computer models are not well represented by stationary Gaussian processes models. Deep Gaussian processes have been shown to be capable of capturing non-stationary behaviors and abrupt regime changes in the computer model response. In this paper, we explore the properties of two deep Gaussian process formulations within the context of computer model emulation. For one of these formulations, we introduce a new parameter that controls the amount of smoothness in the deep Gaussian process layers. We adapt a stochastic variational approach to inference for this model, allowing for prior specification and posterior exploration of the smoothness of the response surface. Our approach can be applied to a large class of computer models, and scales to arbitrarily large simulation designs. The proposed methodology was motivated by the need to emulate an astrophysical model of the formation of binary black hole mergers.