# Stochastic spectral embedding

arXiv: https://arxiv.org/abs/2004.04480 · HTML: https://mlsanity.com/paper/2004.04480/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Apr 2020.

## Built on by (most cited first, 8 of 8)

- [Physics-Informed Polynomial Chaos Expansions](https://mlsanity.com/paper/2309.01697/) (2023)
- [A Review of Machine Learning Methods Applied to Structural Dynamics and Vibroacoustic](https://mlsanity.com/paper/2204.06362/) (2022)
- [Active Learning-based Domain Adaptive Localized Polynomial Chaos Expansion](https://mlsanity.com/paper/2301.13635/) (2023)
- [Polynomial Chaos Surrogate Construction for Random Fields with Parametric Uncertainty](https://mlsanity.com/paper/2311.00553/) (2023)
- [Rare event estimation using stochastic spectral embedding](https://mlsanity.com/paper/2106.05824/) (2021)
- [Dimensionality reduction can be used as a surrogate model for high-dimensional forward uncertainty quantification](https://mlsanity.com/paper/2402.04582/) (2024)
- [Multielement polynomial chaos Kriging-based metamodelling for Bayesian inference of non-smooth systems](https://mlsanity.com/paper/2212.02250/) (2022)
- [Multi-level informed optimization via decomposed Kriging for large design problems under uncertainty](https://mlsanity.com/paper/2510.07904/) (2025)

## Abstract (arXiv)

Constructing approximations that can accurately mimic the behavior of complex models at reduced computational costs is an important aspect of uncertainty quantification. Despite their flexibility and efficiency, classical surrogate models such as Kriging or polynomial chaos expansions tend to struggle with highly non-linear, localized or non-stationary computational models. We hereby propose a novel sequential adaptive surrogate modeling method based on recursively embedding locally spectral expansions. It is achieved by means of disjoint recursive partitioning of the input domain, which consists in sequentially splitting the latter into smaller subdomains, and constructing a simpler local spectral expansions in each, exploiting the trade-off complexity vs. locality. The resulting expansion, which we refer to as "stochastic spectral embedding" (SSE), is a piece-wise continuous approximation of the model response that shows promising approximation capabilities, and good scaling with both the problem dimension and the size of the training set. We finally show how the method compares favorably against state-of-the-art sparse polynomial chaos expansions on a set of models with different complexity and input dimension.