# Analysis and Reduction of Complex Networks Under Uncertainty.

## Abstract

This effort was a collaboration with Youssef Marzouk of MIT, Omar Knio of Duke University (at the time at Johns Hopkins University) and Habib Najm of Sandia National Laboratories. The objective of this effort was to develop the mathematical and algorithmic capacity to analyze complex networks under uncertainty. Of interest were chemical reaction networks and smart grid networks. The statements of work for USC focused on the development of stochastic reduced models for uncertain networks. The USC team was led by Professor Roger Ghanem and consisted of one graduate student and a postdoc. The contributions completed by the USC team consisted of 1) methodology and algorithms to address the eigenvalue problem, a problem of significance in the stability of networks under stochastic perturbations, 2) methodology and algorithms to characterize probability measures on graph structures with random flows. This is an important problem in characterizing random demand (encountered in smart grid) and random degradation (encountered in infrastructure systems), as well as modeling errors in Markov Chains (with ubiquitous relevance !). 3) methodology and algorithms for treating inequalities in uncertain systems. This is an important problem in the context of models for material failure and network flows under uncertainty where conditions ofmore »

- Authors:

- University of Southern California

- Publication Date:

- Research Org.:
- University of Southern California

- Sponsoring Org.:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)USDOE Advanced Research Projects Agency - Energy (ARPA-E)

- Contributing Org.:
- University of Southern California

- OSTI Identifier:
- 1148680

- Report Number(s):
- DOE-USC-SC0003452

- DOE Contract Number:
- SC0003452

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING; Uncertainty Quantification; Networks; Polynomial Chaos; Random Matrix, Random Eigenvalue; Markov Chains.

### Citation Formats

```
Ghanem, Roger G.
```*Analysis and Reduction of Complex Networks Under Uncertainty.*. United States: N. p., 2014.
Web. doi:10.2172/1148680.

```
Ghanem, Roger G.
```*Analysis and Reduction of Complex Networks Under Uncertainty.*. United States. doi:10.2172/1148680.

```
Ghanem, Roger G. Thu .
"Analysis and Reduction of Complex Networks Under Uncertainty.". United States.
doi:10.2172/1148680. https://www.osti.gov/servlets/purl/1148680.
```

```
@article{osti_1148680,
```

title = {Analysis and Reduction of Complex Networks Under Uncertainty.},

author = {Ghanem, Roger G},

abstractNote = {This effort was a collaboration with Youssef Marzouk of MIT, Omar Knio of Duke University (at the time at Johns Hopkins University) and Habib Najm of Sandia National Laboratories. The objective of this effort was to develop the mathematical and algorithmic capacity to analyze complex networks under uncertainty. Of interest were chemical reaction networks and smart grid networks. The statements of work for USC focused on the development of stochastic reduced models for uncertain networks. The USC team was led by Professor Roger Ghanem and consisted of one graduate student and a postdoc. The contributions completed by the USC team consisted of 1) methodology and algorithms to address the eigenvalue problem, a problem of significance in the stability of networks under stochastic perturbations, 2) methodology and algorithms to characterize probability measures on graph structures with random flows. This is an important problem in characterizing random demand (encountered in smart grid) and random degradation (encountered in infrastructure systems), as well as modeling errors in Markov Chains (with ubiquitous relevance !). 3) methodology and algorithms for treating inequalities in uncertain systems. This is an important problem in the context of models for material failure and network flows under uncertainty where conditions of failure or flow are described in the form of inequalities between the state variables.},

doi = {10.2172/1148680},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Thu Jul 31 00:00:00 EDT 2014},

month = {Thu Jul 31 00:00:00 EDT 2014}

}