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

TL;DR

This paper introduces a novel method for representing random fields by rotating the basis of their Wiener Chaos expansions, reducing dimensionality and capturing intermediate features through basis adaptation and projection.

Contribution

It proposes a basis rotation technique within Wiener Chaos expansions to achieve lower-dimensional, more efficient representations of random fields in physical models.

Findings

Reduced the complexity of random field representations.

Captured intermediate characteristics with a mesoscale approach.

Enhanced the efficiency of probabilistic modeling.

Abstract

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.