# AL-SPCE - Reliability analysis for nondeterministic models using stochastic polynomial chaos expansions and active learning

arXiv: https://arxiv.org/abs/2507.04553 · HTML: https://mlsanity.com/paper/2507.04553/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 64 references that are in the map.
- First posted on arXiv 6 Jul 2025.

## Builds on (most cited first, 14 of 14)

- [Practical heteroskedastic Gaussian process modeling for large simulation experiments](https://mlsanity.com/paper/1611.05902/) (2016)
- [Active learning for structural reliability: survey, general framework and benchmark](https://mlsanity.com/paper/2106.01713/) (2021)
- [An active-learning algorithm that combines sparse polynomial chaos expansions and bootstrap for structural reliability analysis](https://mlsanity.com/paper/1709.01589/) (2017)
- [Automatic selection of basis-adaptive sparse polynomial chaos expansions for engineering applications](https://mlsanity.com/paper/2009.04800/) (2020)
- [An Overview of Agent-based Traffic Simulators](https://mlsanity.com/paper/2102.07505/) (2021)
- [Replication-based emulation of the response distribution of stochastic simulators using generalized lambda distributions](https://mlsanity.com/paper/1911.09067/) (2019)
- [Emulation of stochastic simulators using generalized lambda models](https://mlsanity.com/paper/2007.00996/) (2020)
- [A spectral surrogate model for stochastic simulators computed from trajectory samples](https://mlsanity.com/paper/2207.05653/) (2022)
- [Seismic fragility analysis using stochastic polynomial chaos expansions](https://mlsanity.com/paper/2208.07747/) (2022)
- [Polynomial Chaos Surrogate Construction for Random Fields with Parametric Uncertainty](https://mlsanity.com/paper/2311.00553/) (2023)
- [Cross-Entropy Based Importance Sampling for Stochastic Simulation Models](https://mlsanity.com/paper/1804.09305/) (2018)
- [Convergence of Successive Linear Programming Algorithms for Noisy Functions](https://mlsanity.com/paper/2302.07205/) (2023)
- [Reliability analysis for data-driven noisy models using active learning](https://mlsanity.com/paper/2401.10796/) (2024)
- [Reliability analysis for non-deterministic limit-states using stochastic emulators](https://mlsanity.com/paper/2412.13731/) (2024)

## Built on by (most cited first, 1 of 1)

- [High-dimensional reliability-based design optimization using stochastic emulators](https://mlsanity.com/paper/2604.05759/) (2026)

## Abstract (arXiv)

Reliability analysis traditionally relies on deterministic simulators, where identical inputs yield identical outputs. However, many real-world systems exhibit stochastic behavior, producing non-repeatable outcomes even under identical conditions. Stochastic simulators account for this behavior by representing the response as a random variable, whose intrinsic variability must be considered in reliability analysis. While Monte Carlo simulation can address this problem, its computational cost is often prohibitive. Stochastic emulators have therefore been introduced as surrogate models capable of reproducing the random simulator response at reduced cost. Recent studies have shown their potential for reliability analysis, but accurate estimates may still require relatively large training sets, which can be impractical for expensive models. In this work, we propose an active learning framework to further reduce the computational effort. Focusing on stochastic polynomial chaos expansions (SPCE), we introduce a learning function that identifies regions relevant to reliability estimation where the emulator exhibits high predictive uncertainty. We further exploit the asymptotic normality of the maximum likelihood estimator to quantify local prediction uncertainty. The resulting methodology, termed active learning stochastic polynomial chaos expansions (AL-SPCE), is validated on three types of problems. In all cases, AL-SPCE significantly improves computational efficiency compared with previous surrogate-based approaches and direct Monte Carlo simulation, while maintaining accurate reliability estimates.