# Final Report, DOE Early Career Award: Predictive modeling of complex physical systems: new tools for statistical inference, uncertainty quantification, and experimental design

## Abstract

Predictive simulation of complex physical systems increasingly rests on the interplay of experimental observations with computational models. Key inputs, parameters, or structural aspects of models may be incomplete or unknown, and must be developed from indirect and limited observations. At the same time, quantified uncertainties are needed to qualify computational predictions in the support of design and decision-making. In this context, Bayesian statistics provides a foundation for inference from noisy and limited data, but at prohibitive computional expense. This project intends to make rigorous predictive modeling *feasible* in complex physical systems, via accelerated and scalable tools for uncertainty quantification, Bayesian inference, and experimental design. Specific objectives are as follows: 1. Develop adaptive posterior approximations and dimensionality reduction approaches for Bayesian inference in high-dimensional nonlinear systems. 2. Extend accelerated Bayesian methodologies to large-scale {\em sequential} data assimilation, fully treating nonlinear models and non-Gaussian state and parameter distributions. 3. Devise efficient surrogate-based methods for Bayesian model selection and the learning of model structure. 4. Develop scalable simulation/optimization approaches to nonlinear Bayesian experimental design, for both parameter inference and model selection. 5. Demonstrate these inferential tools on chemical kinetic models in reacting flow, constructing and refining thermochemical and electrochemical models from limited data.more »

- Authors:

- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

- Publication Date:

- Research Org.:
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)

- OSTI Identifier:
- 1312896

- Report Number(s):
- DOE-MIT-03908

DE-FG02-10ER25978

- DOE Contract Number:
- SC0003908

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING; Uncertainty quantification; Bayesian inference; sampling; optimal experimental design; optimal transport

### Citation Formats

```
Marzouk, Youssef.
```*Final Report, DOE Early Career Award: Predictive modeling of complex physical systems: new tools for statistical inference, uncertainty quantification, and experimental design*. United States: N. p., 2016.
Web. doi:10.2172/1312896.

```
Marzouk, Youssef.
```*Final Report, DOE Early Career Award: Predictive modeling of complex physical systems: new tools for statistical inference, uncertainty quantification, and experimental design*. United States. doi:10.2172/1312896.

```
Marzouk, Youssef. Wed .
"Final Report, DOE Early Career Award: Predictive modeling of complex physical systems: new tools for statistical inference, uncertainty quantification, and experimental design". United States. doi:10.2172/1312896. https://www.osti.gov/servlets/purl/1312896.
```

```
@article{osti_1312896,
```

title = {Final Report, DOE Early Career Award: Predictive modeling of complex physical systems: new tools for statistical inference, uncertainty quantification, and experimental design},

author = {Marzouk, Youssef},

abstractNote = {Predictive simulation of complex physical systems increasingly rests on the interplay of experimental observations with computational models. Key inputs, parameters, or structural aspects of models may be incomplete or unknown, and must be developed from indirect and limited observations. At the same time, quantified uncertainties are needed to qualify computational predictions in the support of design and decision-making. In this context, Bayesian statistics provides a foundation for inference from noisy and limited data, but at prohibitive computional expense. This project intends to make rigorous predictive modeling *feasible* in complex physical systems, via accelerated and scalable tools for uncertainty quantification, Bayesian inference, and experimental design. Specific objectives are as follows: 1. Develop adaptive posterior approximations and dimensionality reduction approaches for Bayesian inference in high-dimensional nonlinear systems. 2. Extend accelerated Bayesian methodologies to large-scale {\em sequential} data assimilation, fully treating nonlinear models and non-Gaussian state and parameter distributions. 3. Devise efficient surrogate-based methods for Bayesian model selection and the learning of model structure. 4. Develop scalable simulation/optimization approaches to nonlinear Bayesian experimental design, for both parameter inference and model selection. 5. Demonstrate these inferential tools on chemical kinetic models in reacting flow, constructing and refining thermochemical and electrochemical models from limited data. Demonstrate Bayesian filtering on canonical stochastic PDEs and in the dynamic estimation of inhomogeneous subsurface properties and flow fields.},

doi = {10.2172/1312896},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2016},

month = {8}

}