# An active-learning algorithm that combines sparse polynomial chaos expansions and bootstrap for structural reliability analysis

arXiv: https://arxiv.org/abs/1709.01589 · HTML: https://mlsanity.com/paper/1709.01589/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Sep 2017.

## Built on by (most cited first, 14 of 14)

- [Active learning for structural reliability: survey, general framework and benchmark](https://mlsanity.com/paper/2106.01713/) (2021)
- [Active Learning-based Domain Adaptive Localized Polynomial Chaos Expansion](https://mlsanity.com/paper/2301.13635/) (2023)
- [Rare event estimation using stochastic spectral embedding](https://mlsanity.com/paper/2106.05824/) (2021)
- [On Active Learning for Gaussian Process-based Global Sensitivity Analysis](https://mlsanity.com/paper/2308.14220/) (2023)
- [Dimensionality reduction can be used as a surrogate model for high-dimensional forward uncertainty quantification](https://mlsanity.com/paper/2402.04582/) (2024)
- [Reliability analysis for non-deterministic limit-states using stochastic emulators](https://mlsanity.com/paper/2412.13731/) (2024)
- [Reliability analysis of discrete-state performance functions via adaptive sequential sampling with detection of failure surfaces](https://mlsanity.com/paper/2208.02475/) (2022)
- [Uncertainty-aware multi-fidelity surrogate modeling with noisy data](https://mlsanity.com/paper/2401.06447/) (2024)
- [AL-SPCE - Reliability analysis for nondeterministic models using stochastic polynomial chaos expansions and active learning](https://mlsanity.com/paper/2507.04553/) (2025)
- [Conformal prediction for full and sparse polynomial chaos expansions](https://mlsanity.com/paper/2601.16636/) (2026)
- [Conformalized Polynomial Chaos Expansion for Uncertainty-aware Surrogate Modeling](https://mlsanity.com/paper/2510.22375/) (2025)
- [CoNBONet: Conformalized Neuroscience-inspired Bayesian Operator Network for Reliability Analysis](https://mlsanity.com/paper/2603.21678/) (2026)
- [Uncertainty Quantification of Engineering Structures by Polynomial Chaos Expansion and Multivariate Active Learning](https://mlsanity.com/paper/2606.17233/) (2026)
- [AK-MCS-C2 : Active Kriging Monte Carlo Simulation method with conformal certification for failure probability estimation](https://mlsanity.com/paper/2606.20191/) (2026)

## Abstract (arXiv)

Polynomial chaos expansions (PCE) have seen widespread use in the context of uncertainty quantification. However, their application to structural reliability problems has been hindered by the limited performance of PCE in the tails of the model response and due to the lack of local metamodel error estimates. We propose a new method to provide local metamodel error estimates based on bootstrap resampling and sparse PCE. An initial experimental design is iteratively updated based on the current estimation of the limit-state surface in an active learning algorithm. The greedy algorithm uses the bootstrap-based local error estimates for the polynomial chaos predictor to identify the best candidate set of points to enrich the experimental design. We demonstrate the effectiveness of this approach on a well-known analytical benchmark representing a series system, on a truss structure and on a complex realistic frame structure problem.