# Sliced-Inverse-Regression--Aided Rotated Compressive Sensing Method for Uncertainty Quantification

## Abstract

Compressive-sensing-based uncertainty quantification methods have become a pow- erful tool for problems with limited data. In this paper, we use the sliced inverse regression (SIR) method to provide an initial guess for the alternating direction method, which is used to enhance sparsity of the Hermite polynomial expansion of stochastic state variables. The sparsity improvement increases both the efficiency and accuracy of the compressive-sensing-based uncertainty quantification method. We demonstrate that the initial guess from SIR is more suitable for the cases when the available data is very limited (Algorithm 4). We also propose another algorithm (Algorithm 5) that performs dimension reduction first with sliced inverse regression, then constructs a Hermite polynomial expansion of the reduced model. This method allows us to approximate the statistics accurately with even less available data. Both methods are non-intrusive and require no a priori information of the sparsity of the system. We demonstrate the effectiveness of these two methods (Algorithms 4 and 5) using problems with up to 500 random dimensions.

- Authors:

- Publication Date:

- Research Org.:
- Pacific Northwest National Lab. (PNNL), Richland, WA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1497679

- Report Number(s):
- PNNL-SA-129338

Journal ID: ISSN 2166-2525

- DOE Contract Number:
- AC05-76RL01830

- Resource Type:
- Journal Article

- Journal Name:
- SIAM/ASA Journal on Uncertainty Quantification

- Additional Journal Information:
- Journal Volume: 6; Journal Issue: 4; Journal ID: ISSN 2166-2525

- Publisher:
- SIAM

- Country of Publication:
- United States

- Language:
- English

### Citation Formats

```
Yang, Xiu, Li, Weixuan, and Tartakovsky, Alexandre.
```*Sliced-Inverse-Regression--Aided Rotated Compressive Sensing Method for Uncertainty Quantification*. United States: N. p., 2018.
Web. doi:10.1137/17M1148955.

```
Yang, Xiu, Li, Weixuan, & Tartakovsky, Alexandre.
```*Sliced-Inverse-Regression--Aided Rotated Compressive Sensing Method for Uncertainty Quantification*. United States. doi:10.1137/17M1148955.

```
Yang, Xiu, Li, Weixuan, and Tartakovsky, Alexandre. Mon .
"Sliced-Inverse-Regression--Aided Rotated Compressive Sensing Method for Uncertainty Quantification". United States. doi:10.1137/17M1148955.
```

```
@article{osti_1497679,
```

title = {Sliced-Inverse-Regression--Aided Rotated Compressive Sensing Method for Uncertainty Quantification},

author = {Yang, Xiu and Li, Weixuan and Tartakovsky, Alexandre},

abstractNote = {Compressive-sensing-based uncertainty quantification methods have become a pow- erful tool for problems with limited data. In this paper, we use the sliced inverse regression (SIR) method to provide an initial guess for the alternating direction method, which is used to enhance sparsity of the Hermite polynomial expansion of stochastic state variables. The sparsity improvement increases both the efficiency and accuracy of the compressive-sensing-based uncertainty quantification method. We demonstrate that the initial guess from SIR is more suitable for the cases when the available data is very limited (Algorithm 4). We also propose another algorithm (Algorithm 5) that performs dimension reduction first with sliced inverse regression, then constructs a Hermite polynomial expansion of the reduced model. This method allows us to approximate the statistics accurately with even less available data. Both methods are non-intrusive and require no a priori information of the sparsity of the system. We demonstrate the effectiveness of these two methods (Algorithms 4 and 5) using problems with up to 500 random dimensions.},

doi = {10.1137/17M1148955},

journal = {SIAM/ASA Journal on Uncertainty Quantification},

issn = {2166-2525},

number = 4,

volume = 6,

place = {United States},

year = {2018},

month = {1}

}