# Polynomial Chaos Surrogate Construction for Random Fields with Parametric Uncertainty

arXiv: https://arxiv.org/abs/2311.00553 · HTML: https://mlsanity.com/paper/2311.00553/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 69 references that are in the map.
- First posted on arXiv 1 Nov 2023.

## Builds on (most cited first, 10 of 10)

- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Sparse Polynomial Chaos Expansions: Literature Survey and Benchmark](https://mlsanity.com/paper/2002.01290/) (2020)
- [Practical heteroskedastic Gaussian process modeling for large simulation experiments](https://mlsanity.com/paper/1611.05902/) (2016)
- [Data-driven polynomial chaos expansion for machine learning regression](https://mlsanity.com/paper/1808.03216/) (2018)
- [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)
- [Stochastic spectral embedding](https://mlsanity.com/paper/2004.04480/) (2020)
- [A spectral surrogate model for stochastic simulators computed from trajectory samples](https://mlsanity.com/paper/2207.05653/) (2022)
- [Emulators for stochastic simulation codes](https://mlsanity.com/paper/1406.6348/) (2014)
- [Global sensitivity analysis for stochastic simulators based on generalized lambda surrogate models](https://mlsanity.com/paper/2005.01309/) (2020)

## Built on by (most cited first, 3 of 3)

- [AL-SPCE - Reliability analysis for nondeterministic models using stochastic polynomial chaos expansions and active learning](https://mlsanity.com/paper/2507.04553/) (2025)
- [MF-GLaM: A multifidelity stochastic emulator using generalized lambda models](https://mlsanity.com/paper/2507.10303/) (2025)
- [Bifidelity Karhunen-Lo`eve Expansion Surrogate with Active Learning for Random Fields](https://mlsanity.com/paper/2511.03756/) (2025)

## Abstract (arXiv)

Engineering and applied science rely on computational experiments to rigorously study physical systems. The mathematical models used to probe these systems are highly complex, and sampling-intensive studies often require prohibitively many simulations for acceptable accuracy. Surrogate models provide a means of circumventing the high computational expense of sampling such complex models. In particular, polynomial chaos expansions (PCEs) have been successfully used for uncertainty quantification studies of deterministic models where the dominant source of uncertainty is parametric. We discuss an extension to conventional PCE surrogate modeling to enable surrogate construction for stochastic computational models that have intrinsic noise in addition to parametric uncertainty. We develop a PCE surrogate on a joint space of intrinsic and parametric uncertainty, enabled by Rosenblatt transformations, and then extend the construction to random field data via the Karhunen-Loeve expansion. We then take advantage of closed-form solutions for computing PCE Sobol indices to perform a global sensitivity analysis of the model which quantifies the intrinsic noise contribution to the overall model output variance. Additionally, the resulting joint PCE is generative in the sense that it allows generating random realizations at any input parameter setting that are statistically approximately equivalent to realizations from the underlying stochastic model. The method is demonstrated on a chemical catalysis example model.