# Development of an exchange–correlation functional with uncertainty quantification capabilities for density functional theory

## Abstract

This paper presents the development of a new exchange–correlation functional from the point of view of machine learning. Using atomization energies of solids and small molecules, we train a linear model for the exchange enhancement factor using a Bayesian approach which allows for the quantification of uncertainties in the predictions. A relevance vector machine is used to automatically select the most relevant terms of the model. We then test this model on atomization energies and also on bulk properties. The average model provides a mean absolute error of only 0.116 eV for the test points of the G2/97 set but a larger 0.314 eV for the test solids. In terms of bulk properties, the prediction for transition metals and monovalent semiconductors has a very low test error. However, as expected, predictions for types of materials not represented in the training set such as ionic solids show much larger errors.

- Authors:

- Publication Date:

- OSTI Identifier:
- 22570241

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Computational Physics; Journal Volume: 311; Other Information: Copyright (c) 2016 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ATOMIZATION; CORRELATIONS; DENSITY FUNCTIONAL METHOD; ERRORS; FORECASTING; MOLECULES; SEMICONDUCTOR MATERIALS; SOLIDS; TRANSITION ELEMENTS

### Citation Formats

```
Aldegunde, Manuel, E-mail: M.A.Aldegunde-Rodriguez@warwick.ac.uk, Kermode, James R., E-mail: J.R.Kermode@warwick.ac.uk, and Zabaras, Nicholas.
```*Development of an exchange–correlation functional with uncertainty quantification capabilities for density functional theory*. United States: N. p., 2016.
Web. doi:10.1016/J.JCP.2016.01.034.

```
Aldegunde, Manuel, E-mail: M.A.Aldegunde-Rodriguez@warwick.ac.uk, Kermode, James R., E-mail: J.R.Kermode@warwick.ac.uk, & Zabaras, Nicholas.
```*Development of an exchange–correlation functional with uncertainty quantification capabilities for density functional theory*. United States. doi:10.1016/J.JCP.2016.01.034.

```
Aldegunde, Manuel, E-mail: M.A.Aldegunde-Rodriguez@warwick.ac.uk, Kermode, James R., E-mail: J.R.Kermode@warwick.ac.uk, and Zabaras, Nicholas. Fri .
"Development of an exchange–correlation functional with uncertainty quantification capabilities for density functional theory". United States. doi:10.1016/J.JCP.2016.01.034.
```

```
@article{osti_22570241,
```

title = {Development of an exchange–correlation functional with uncertainty quantification capabilities for density functional theory},

author = {Aldegunde, Manuel, E-mail: M.A.Aldegunde-Rodriguez@warwick.ac.uk and Kermode, James R., E-mail: J.R.Kermode@warwick.ac.uk and Zabaras, Nicholas},

abstractNote = {This paper presents the development of a new exchange–correlation functional from the point of view of machine learning. Using atomization energies of solids and small molecules, we train a linear model for the exchange enhancement factor using a Bayesian approach which allows for the quantification of uncertainties in the predictions. A relevance vector machine is used to automatically select the most relevant terms of the model. We then test this model on atomization energies and also on bulk properties. The average model provides a mean absolute error of only 0.116 eV for the test points of the G2/97 set but a larger 0.314 eV for the test solids. In terms of bulk properties, the prediction for transition metals and monovalent semiconductors has a very low test error. However, as expected, predictions for types of materials not represented in the training set such as ionic solids show much larger errors.},

doi = {10.1016/J.JCP.2016.01.034},

journal = {Journal of Computational Physics},

number = ,

volume = 311,

place = {United States},

year = {Fri Apr 15 00:00:00 EDT 2016},

month = {Fri Apr 15 00:00:00 EDT 2016}

}