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

## 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.

- Authors:

- Department of Mathematics, University of Southern California, Los Angeles, CA 90089 (United States)
- (United States)
- Department of Civil Engineering, University of Southern California, Los Angeles, CA 90089 (United States)

- Publication Date:

- OSTI Identifier:
- 22622307

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Computational Physics; Journal Volume: 341; Other Information: Copyright (c) 2017 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CAPTURE; CHAOS THEORY; COMPUTERIZED SIMULATION; EXPANSION; GAUSSIAN PROCESSES; HILBERT SPACE; POLYNOMIALS; PROBABILITY; RANDOMNESS; REDUCTION; ROTATION

### Citation Formats

```
Tsilifis, Panagiotis, E-mail: tsilifis@usc.edu, Department of Civil Engineering, University of Southern California, Los Angeles, CA 90089, and Ghanem, Roger G., E-mail: ghanem@usc.edu.
```*Reduced Wiener Chaos representation of random fields via basis adaptation and projection*. United States: N. p., 2017.
Web. doi:10.1016/J.JCP.2017.04.009.

```
Tsilifis, Panagiotis, E-mail: tsilifis@usc.edu, Department of Civil Engineering, University of Southern California, Los Angeles, CA 90089, & Ghanem, Roger G., E-mail: ghanem@usc.edu.
```*Reduced Wiener Chaos representation of random fields via basis adaptation and projection*. United States. doi:10.1016/J.JCP.2017.04.009.

```
Tsilifis, Panagiotis, E-mail: tsilifis@usc.edu, Department of Civil Engineering, University of Southern California, Los Angeles, CA 90089, and Ghanem, Roger G., E-mail: ghanem@usc.edu. Sat .
"Reduced Wiener Chaos representation of random fields via basis adaptation and projection". United States.
doi:10.1016/J.JCP.2017.04.009.
```

```
@article{osti_22622307,
```

title = {Reduced Wiener Chaos representation of random fields via basis adaptation and projection},

author = {Tsilifis, Panagiotis, E-mail: tsilifis@usc.edu and Department of Civil Engineering, University of Southern California, Los Angeles, CA 90089 and Ghanem, Roger G., E-mail: ghanem@usc.edu},

abstractNote = {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.},

doi = {10.1016/J.JCP.2017.04.009},

journal = {Journal of Computational Physics},

number = ,

volume = 341,

place = {United States},

year = {Sat Jul 15 00:00:00 EDT 2017},

month = {Sat Jul 15 00:00:00 EDT 2017}

}

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