# Entropy-based adaptive design for contour finding and estimating reliability

arXiv: https://arxiv.org/abs/2105.11357 · HTML: https://mlsanity.com/paper/2105.11357/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 79 references that are in the map.
- First posted on arXiv 24 May 2021.

## Builds on (most cited first, 9 of 9)

- [Survey of multifidelity methods in uncertainty propagation, inference, and optimization](https://mlsanity.com/paper/1806.10761/) (2018)
- [Local Gaussian process approximation for large computer experiments](https://mlsanity.com/paper/1303.0383/) (2013)
- [Bayesian Optimization with Gradients](https://mlsanity.com/paper/1703.04389/) (2017)
- [Truncated Variance Reduction: A Unified Approach to Bayesian Optimization and Level-Set Estimation](https://mlsanity.com/paper/1610.07379/) (2016)
- [Adaptive Design of Experiments for Conservative Estimation of Excursion Sets](https://mlsanity.com/paper/1611.07256/) (2016)
- [Contour location via entropy reduction leveraging multiple information sources](https://mlsanity.com/paper/1805.07489/) (2018)
- [Evaluating Gaussian Process Metamodels and Sequential Designs for Noisy Level Set Estimation](https://mlsanity.com/paper/1807.06712/) (2018)
- [Distance-distributed design for Gaussian process surrogates](https://mlsanity.com/paper/1812.02794/) (2018)
- [Quantifying uncertainties on excursion sets under a Gaussian random field prior](https://mlsanity.com/paper/1501.03659/) (2015)

## Built on by (most cited first, 10 of 10)

- [Bayesian Active Learning with Fully Bayesian Gaussian Processes](https://mlsanity.com/paper/2205.10186/) (2022)
- [Triangulation candidates for Bayesian optimization](https://mlsanity.com/paper/2112.07457/) (2021)
- [Bayesian sequential design of computer experiments for quantile set inversion](https://mlsanity.com/paper/2211.01008/) (2022)
- [CRPS-Based Targeted Sequential Design with Application in Chemical Space](https://mlsanity.com/paper/2503.11250/) (2025)
- [Informed Initialization for Bayesian Optimization and Active Learning](https://mlsanity.com/paper/2510.23681/) (2025)
- [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)
- [An (ε,δ)-accurate level set estimation with a stopping criterion](https://mlsanity.com/paper/2503.20272/) (2025)
- [Bayesian Active Learning of (small) Quantile Sets through Expected Estimator Modification](https://mlsanity.com/paper/2506.13211/) (2025)
- [Actively Learning Joint Contours of Multiple Computer Experiments](https://mlsanity.com/paper/2512.13530/) (2025)

## Abstract (arXiv)

In reliability analysis, methods used to estimate failure probability are often limited by the costs associated with model evaluations. Many of these methods, such as multifidelity importance sampling (MFIS), rely upon a computationally efficient, surrogate model like a Gaussian process (GP) to quickly generate predictions. The quality of the GP fit, particularly in the vicinity of the failure region(s), is instrumental in supplying accurately predicted failures for such strategies. We introduce an entropy-based GP adaptive design that, when paired with MFIS, provides more accurate failure probability estimates and with higher confidence. We show that our greedy data acquisition strategy better identifies multiple failure regions compared to existing contour-finding schemes. We then extend the method to batch selection, without sacrificing accuracy. Illustrative examples are provided on benchmark data as well as an application to an impact damage simulator for National Aeronautics and Space Administration (NASA) spacesuits.