# Mathematical Foundations for Uncertainty Quantification in Materials Design. Final Report

## Abstract

Final report DE-SC0010723. Our key accomplishment in the first year of the grant is that we started developing pathwise information theory-based and goal-oriented sensitivity analysis and parameter identification methods for complex high-dimensional dynamics and in particular of nonequilibrium extended systems. The combination of these novel methodologies provide the first methods in the literature which are capable to handle UQ questions for stochastic complex systems with some or all of the following features: (a) multi-scale models with a very large number of parameters, (b) spatially distributed systems such as Kinetic Monte Carlo or Langevin Dynamics, (c) non-equilibrium processes typically associated with coupled physico-chemical mechanisms, driven boundary conditions, etc. The first two such publications sponsored by the grant, have just been published.

- Authors:

- Univ. of Massachusetts, Amherst, MA (United States)

- Publication Date:

- Research Org.:
- Univ. of Massachusetts, Amherst, MA (United States)

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

- Contributing Org.:
- Brown University; University of Delaware

- OSTI Identifier:
- 1483471

- Report Number(s):
- FinalReport

- DOE Contract Number:
- SC0010723

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 36 MATERIALS SCIENCE; 97 MATHEMATICS AND COMPUTING

### Citation Formats

```
Katsoulakis, Markos A., and Rey-Bellet, Luc.
```*Mathematical Foundations for Uncertainty Quantification in Materials Design. Final Report*. United States: N. p., 2018.
Web. doi:10.2172/1483471.

```
Katsoulakis, Markos A., & Rey-Bellet, Luc.
```*Mathematical Foundations for Uncertainty Quantification in Materials Design. Final Report*. United States. doi:10.2172/1483471.

```
Katsoulakis, Markos A., and Rey-Bellet, Luc. Tue .
"Mathematical Foundations for Uncertainty Quantification in Materials Design. Final Report". United States. doi:10.2172/1483471. https://www.osti.gov/servlets/purl/1483471.
```

```
@article{osti_1483471,
```

title = {Mathematical Foundations for Uncertainty Quantification in Materials Design. Final Report},

author = {Katsoulakis, Markos A. and Rey-Bellet, Luc},

abstractNote = {Final report DE-SC0010723. Our key accomplishment in the first year of the grant is that we started developing pathwise information theory-based and goal-oriented sensitivity analysis and parameter identification methods for complex high-dimensional dynamics and in particular of nonequilibrium extended systems. The combination of these novel methodologies provide the first methods in the literature which are capable to handle UQ questions for stochastic complex systems with some or all of the following features: (a) multi-scale models with a very large number of parameters, (b) spatially distributed systems such as Kinetic Monte Carlo or Langevin Dynamics, (c) non-equilibrium processes typically associated with coupled physico-chemical mechanisms, driven boundary conditions, etc. The first two such publications sponsored by the grant, have just been published.},

doi = {10.2172/1483471},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2018},

month = {11}

}