# Bayesian Regression of Thermodynamic Models of Redox Active Materials

## Abstract

Finding a suitable functional redox material is a critical challenge to achieving scalable, economically viable technologies for storing concentrated solar energy in the form of a defected oxide. Demonstrating e ectiveness for thermal storage or solar fuel is largely accomplished by using a thermodynamic model derived from experimental data. The purpose of this project is to test the accuracy of our regression model on representative data sets. Determining the accuracy of the model includes parameter tting the model to the data, comparing the model using di erent numbers of param- eters, and analyzing the entropy and enthalpy calculated from the model. Three data sets were considered in this project: two demonstrating materials for solar fuels by wa- ter splitting and the other of a material for thermal storage. Using Bayesian Inference and Markov Chain Monte Carlo (MCMC), parameter estimation was preformed on the three data sets. Good results were achieved, except some there was some deviations on the edges of the data input ranges. The evidence values were then calculated in a variety of ways and used to compare models with di erent number of parameters. It was believed that at least one of the parameters was unnecessary and comparingmore »

- Authors:

- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

- Publication Date:

- Research Org.:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

- Sponsoring Org.:
- USDOE Office of Energy Efficiency and Renewable Energy (EERE), Fuel Cell Technologies Office (EE-3F)

- OSTI Identifier:
- 1389915

- Report Number(s):
- SAND2017-9526R

656761

- DOE Contract Number:
- AC04-94AL85000

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; 36 MATERIALS SCIENCE

### Citation Formats

```
Johnston, Katherine.
```*Bayesian Regression of Thermodynamic Models of Redox Active Materials*. United States: N. p., 2017.
Web. doi:10.2172/1389915.

```
Johnston, Katherine.
```*Bayesian Regression of Thermodynamic Models of Redox Active Materials*. United States. doi:10.2172/1389915.

```
Johnston, Katherine. Fri .
"Bayesian Regression of Thermodynamic Models of Redox Active Materials". United States.
doi:10.2172/1389915. https://www.osti.gov/servlets/purl/1389915.
```

```
@article{osti_1389915,
```

title = {Bayesian Regression of Thermodynamic Models of Redox Active Materials},

author = {Johnston, Katherine},

abstractNote = {Finding a suitable functional redox material is a critical challenge to achieving scalable, economically viable technologies for storing concentrated solar energy in the form of a defected oxide. Demonstrating e ectiveness for thermal storage or solar fuel is largely accomplished by using a thermodynamic model derived from experimental data. The purpose of this project is to test the accuracy of our regression model on representative data sets. Determining the accuracy of the model includes parameter tting the model to the data, comparing the model using di erent numbers of param- eters, and analyzing the entropy and enthalpy calculated from the model. Three data sets were considered in this project: two demonstrating materials for solar fuels by wa- ter splitting and the other of a material for thermal storage. Using Bayesian Inference and Markov Chain Monte Carlo (MCMC), parameter estimation was preformed on the three data sets. Good results were achieved, except some there was some deviations on the edges of the data input ranges. The evidence values were then calculated in a variety of ways and used to compare models with di erent number of parameters. It was believed that at least one of the parameters was unnecessary and comparing evidence values demonstrated that the parameter was need on one data set and not signi cantly helpful on another. The entropy was calculated by taking the derivative in one variable and integrating over another. and its uncertainty was also calculated by evaluating the entropy over multiple MCMC samples. Afterwards, all the parts were written up as a tutorial for the Uncertainty Quanti cation Toolkit (UQTk).},

doi = {10.2172/1389915},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Fri Sep 01 00:00:00 EDT 2017},

month = {Fri Sep 01 00:00:00 EDT 2017}

}