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

TL;DR

This paper introduces a novel hybrid criterion for contour location in reliability analysis using deep Gaussian processes, effectively addressing optimization challenges posed by Bayesian inference and enhancing performance in aerospace simulations.

Contribution

It develops a hybrid exploration criterion combining entropy and uncertainty for DGP-based contour location, overcoming derivative-based optimization issues in Bayesian settings.

Findings

Effective in synthetic benchmarks

Successful application to RAE-2822 airfoil simulation

Improves reliability analysis accuracy

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.