Contour Location for Reliability in Airfoil Simulation Experiments using Deep Gaussian Processes

Ashwin Renganathan, Annie S. Booth, Robert B. Gramacy

Abstract:

Bayesian deep Gaussian processes (DGPs) outperform ordinary GPs as surrogate models of complex
computer experiments when response surface dynamics are non-stationary, which is especially prevalent
in aerospace simulations. Yet DGP surrogates have not been deployed for the canonical downstream task
in that setting: reliability analysis through contour location (CL). In that context, we are motivated by
a simulation of an RAE-2822 transonic airfoil which demarcates efficient and inefficient flight conditions.
Level sets separating passable versus failable operating conditions are best learned through strategic
sequential designs. There are two limitations to modern CL methodology which hinder DGP integration in this setting. First, derivative-based optimization underlying acquisition functions is thwarted by
sampling-based Bayesian (i.e., MCMC) inference, which is essential for DGP posterior integration. Second, canonical acquisition criteria, such as entropy, are famously myopic to the extent that optimization
may even be undesirable. Here we tackle both of these limitations at once, proposing a hybrid criterion
that explores along the Pareto front of entropy and (predictive) uncertainty, requiring evaluation only at
strategically located “triangulation” candidates. We showcase DGP CL performance in several synthetic
benchmark exercises and on the RAE-2822 airfoil.