# Rare event estimation using stochastic spectral embedding

arXiv: https://arxiv.org/abs/2106.05824 · HTML: https://mlsanity.com/paper/2106.05824/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 59 references that are in the map.
- First posted on arXiv 9 Jun 2021.

## Builds on (most cited first, 6 of 6)

- [Sparse Polynomial Chaos Expansions: Literature Survey and Benchmark](https://mlsanity.com/paper/2002.01290/) (2020)
- [Data-driven polynomial chaos expansion for machine learning regression](https://mlsanity.com/paper/1808.03216/) (2018)
- [An active-learning algorithm that combines sparse polynomial chaos expansions and bootstrap for structural reliability analysis](https://mlsanity.com/paper/1709.01589/) (2017)
- [Stochastic spectral embedding](https://mlsanity.com/paper/2004.04480/) (2020)
- [Bayesian model inversion using stochastic spectral embedding](https://mlsanity.com/paper/2005.07380/) (2020)
- [A general framework for data-driven uncertainty quantification under complex input dependencies using vine copulas](https://mlsanity.com/paper/1709.08626/) (2017)

## Built on by (most cited first, 2 of 2)

- [Active Learning-based Domain Adaptive Localized Polynomial Chaos Expansion](https://mlsanity.com/paper/2301.13635/) (2023)
- [Automating structural reliability analysis with a multi-agent large language model framework](https://mlsanity.com/paper/2607.16580/) (2026)

## Abstract (arXiv)

Estimating the probability of rare failure events is an essential step in the reliability assessment of engineering systems. Computing this failure probability for complex non-linear systems is challenging, and has recently spurred the development of active-learning reliability methods. These methods approximate the limit-state function (LSF) using surrogate models trained with a sequentially enriched set of model evaluations. A recently proposed method called stochastic spectral embedding (SSE) aims to improve the local approximation accuracy of global, spectral surrogate modelling techniques by sequentially embedding local residual expansions in subdomains of the input space. In this work we apply SSE to the LSF, giving rise to a stochastic spectral embedding-based reliability (SSER) method. The resulting partition of the input space decomposes the failure probability into a set of easy-to-compute revconditional failure probabilities. We propose a set of modifications that tailor the algorithm to efficiently solve rare event estimation problems. These modifications include specialized refinement domain selection, partitioning and enrichment strategies. We showcase the algorithm performance on four benchmark problems of various dimensionality and complexity in the LSF.