# Reduced Wiener Chaos representation of random fields via basis adaptation and projection

arXiv: https://arxiv.org/abs/1603.04803 · HTML: https://mlsanity.com/paper/1603.04803/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Mar 2016.

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

- [A survey of unsupervised learning methods for high-dimensional uncertainty quantification in black-box-type problems](https://mlsanity.com/paper/2202.04648/) (2022)
- [Probabilistic learning inference of boundary value problem with uncertainties based on Kullback-Leibler divergence under implicit constraints](https://mlsanity.com/paper/2202.05112/) (2022)
- [Application of probabilistic modeling and automated machine learning framework for high-dimensional stress field](https://mlsanity.com/paper/2303.16869/) (2023)

## Abstract (arXiv)

A new characterization of random fields appearing in physical models is presented that is based on their well-known Homogeneous Chaos expansions. We take advantage of the adaptation capabilities of these expansions where the core idea is to rotate the basis of the underlying Gaussian Hilbert space, in order to achieve reduced functional representations that concentrate the induced probability measure in a lower dimensional subspace. For a smooth family of rotations along the domain of interest, the uncorrelated Gaussian inputs are transformed into a Gaussian process, thus introducing a mesoscale that captures intermediate characteristics of the quantity of interest.