# Comparing theory based and higher-order reduced models for fusion simulation data

## Abstract

We consider using regression to fit a theory-based log-linear ansatz, as well as higher order approximations, for the thermal energy confinement of a Tokamak as a function of device features. We use general linear models based on total order polynomials, as well as deep neural networks. The results indicate that the theory-based model fits the data almost as well as the more sophisticated machines, within the support of the data set. The conclusion we arrive at is that only negligible improvements can be made to the theoretical model, for input data of this type.

- Authors:

- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- Univ. of Manchester (United Kingdom)
- King Abdullah Univ. of Science and Technology, Thuwal (Saudi Arabia)
- General Atomics, San Diego, CA (United States)

- Publication Date:

- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

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

- OSTI Identifier:
- 1486929

- Grant/Contract Number:
- AC05-00OR22725

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Big Data and Information Analytics (Online)

- Additional Journal Information:
- Journal Name: Big Data and Information Analytics (Online); Journal Volume: 3; Journal Issue: 2; Journal ID: ISSN 2380-6974

- Publisher:
- AIMS Press

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; 97 MATHEMATICS AND COMPUTING

### Citation Formats

```
E. Bernholdt, David, R. Ciancosa, Mark, L. Green, David, J.H. Law, Kody, Litvinenko, Alexander, and M. Park, Jin. Comparing theory based and higher-order reduced models for fusion simulation data. United States: N. p., 2018.
Web. doi:10.3934/BigDIA.2018.2.41.
```

```
E. Bernholdt, David, R. Ciancosa, Mark, L. Green, David, J.H. Law, Kody, Litvinenko, Alexander, & M. Park, Jin. Comparing theory based and higher-order reduced models for fusion simulation data. United States. doi:10.3934/BigDIA.2018.2.41.
```

```
E. Bernholdt, David, R. Ciancosa, Mark, L. Green, David, J.H. Law, Kody, Litvinenko, Alexander, and M. Park, Jin. Thu .
"Comparing theory based and higher-order reduced models for fusion simulation data". United States. doi:10.3934/BigDIA.2018.2.41. https://www.osti.gov/servlets/purl/1486929.
```

```
@article{osti_1486929,
```

title = {Comparing theory based and higher-order reduced models for fusion simulation data},

author = {E. Bernholdt, David and R. Ciancosa, Mark and L. Green, David and J.H. Law, Kody and Litvinenko, Alexander and M. Park, Jin},

abstractNote = {We consider using regression to fit a theory-based log-linear ansatz, as well as higher order approximations, for the thermal energy confinement of a Tokamak as a function of device features. We use general linear models based on total order polynomials, as well as deep neural networks. The results indicate that the theory-based model fits the data almost as well as the more sophisticated machines, within the support of the data set. The conclusion we arrive at is that only negligible improvements can be made to the theoretical model, for input data of this type.},

doi = {10.3934/BigDIA.2018.2.41},

journal = {Big Data and Information Analytics (Online)},

number = 2,

volume = 3,

place = {United States},

year = {2018},

month = {12}

}

Free Publicly Available Full Text

Publisher's Version of Record

Other availability

#### Figures / Tables:

Figure 1: Comparison of true values with GLM prediction, for log linear (left), and log sixth order (right). The right subplots show the error distribution histogram (difference between values of the truth and the prediction). Out-of-sample, test data.

All figures and tables
(7 total)

Save to My Library

You must Sign In or Create an Account in order to save documents to your library.

Figures / Tables found in this record:

*Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.*