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

arXiv: https://arxiv.org/abs/2308.04420 · HTML: https://mlsanity.com/paper/2308.04420/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Aug 2023.

## Built on by (most cited first, 7 of 7)

- [qPOTS: Efficient batch multiobjective Bayesian optimization via Pareto optimal Thompson sampling](https://mlsanity.com/paper/2310.15788/) (2023)
- [Expected Diverse Utility (EDU): Diverse Bayesian Optimization of Expensive Computer Simulators](https://mlsanity.com/paper/2410.01196/) (2024)
- [REMAL: Residual Equilibrium Manifold Active Learning for Surrogate-Based Multidisciplinary Design Analysis](https://mlsanity.com/paper/2606.13245/) (2026)
- [Multifidelity Cross-validation](https://mlsanity.com/paper/2407.01495/) (2024)
- [Active Learning for Multiple Change Point Detection in Non-stationary Time Series with Deep Gaussian Processes](https://mlsanity.com/paper/2505.20452/) (2025)
- [Actively Learning Joint Contours of Multiple Computer Experiments](https://mlsanity.com/paper/2512.13530/) (2025)
- [A Bayesian latent Gaussian process framework for aerodynamic uncertainty quantification](https://mlsanity.com/paper/2606.28871/) (2026)

## Abstract (arXiv)

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.