# Uncertainty quantification for nuclear density functional theory and information content of new measurements

## Abstract

Statistical tools of uncertainty quantification can be used to assess the information content of measured observables with respect to present-day theoretical models, to estimate model errors and thereby improve predictive capability, to extrapolate beyond the regions reached by experiment, and to provide meaningful input to applications and planned measurements. To showcase new opportunities offered by such tools, we make a rigorous analysis of theoretical statistical uncertainties in nuclear density functional theory using Bayesian inference methods. By considering the recent mass measurements from the Canadian Penning Trap at Argonne National Laboratory, we demonstrate how the Bayesian analysis and a direct least-squares optimization, combined with high-performance computing, can be used to assess the information content of the new data with respect to a model based on the Skyrme energy density functional approach. Employing the posterior probability distribution computed with a Gaussian process emulator, we apply the Bayesian framework to propagate theoretical statistical uncertainties in predictions of nuclear masses, two-neutron dripline, and fission barriers. Overall, we find that the new mass measurements do not impose a constraint that is strong enough to lead to significant changes in the model parameters. As a result, the example discussed in this study sets the stage formore »

- Authors:

- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Argonne National Lab. (ANL), Argonne, IL (United States)
- Michigan State Univ., East Lansing, MI (United States); Oak Ridge National Lab., Oak Ridge, TN (United States); Univ. of Warsaw, Warsaw (Poland)

- Publication Date:

- Research Org.:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1179409

- Report Number(s):
- LLNL-JRNL-665886

Journal ID: ISSN 0031-9007; PRLTAO

- DOE Contract Number:
- AC52-07NA27344

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review Letters; Journal Volume: 114; Journal Issue: 12

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; 97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE

### Citation Formats

```
McDonnell, J. D., Schunck, N., Higdon, D., Sarich, J., Wild, S. M., and Nazarewicz, W.
```*Uncertainty quantification for nuclear density functional theory and information content of new measurements*. United States: N. p., 2015.
Web. doi:10.1103/PhysRevLett.114.122501.

```
McDonnell, J. D., Schunck, N., Higdon, D., Sarich, J., Wild, S. M., & Nazarewicz, W.
```*Uncertainty quantification for nuclear density functional theory and information content of new measurements*. United States. doi:10.1103/PhysRevLett.114.122501.

```
McDonnell, J. D., Schunck, N., Higdon, D., Sarich, J., Wild, S. M., and Nazarewicz, W. Tue .
"Uncertainty quantification for nuclear density functional theory and information content of new measurements". United States.
doi:10.1103/PhysRevLett.114.122501. https://www.osti.gov/servlets/purl/1179409.
```

```
@article{osti_1179409,
```

title = {Uncertainty quantification for nuclear density functional theory and information content of new measurements},

author = {McDonnell, J. D. and Schunck, N. and Higdon, D. and Sarich, J. and Wild, S. M. and Nazarewicz, W.},

abstractNote = {Statistical tools of uncertainty quantification can be used to assess the information content of measured observables with respect to present-day theoretical models, to estimate model errors and thereby improve predictive capability, to extrapolate beyond the regions reached by experiment, and to provide meaningful input to applications and planned measurements. To showcase new opportunities offered by such tools, we make a rigorous analysis of theoretical statistical uncertainties in nuclear density functional theory using Bayesian inference methods. By considering the recent mass measurements from the Canadian Penning Trap at Argonne National Laboratory, we demonstrate how the Bayesian analysis and a direct least-squares optimization, combined with high-performance computing, can be used to assess the information content of the new data with respect to a model based on the Skyrme energy density functional approach. Employing the posterior probability distribution computed with a Gaussian process emulator, we apply the Bayesian framework to propagate theoretical statistical uncertainties in predictions of nuclear masses, two-neutron dripline, and fission barriers. Overall, we find that the new mass measurements do not impose a constraint that is strong enough to lead to significant changes in the model parameters. As a result, the example discussed in this study sets the stage for quantifying and maximizing the impact of new measurements with respect to current modeling and guiding future experimental efforts, thus enhancing the experiment-theory cycle in the scientific method.},

doi = {10.1103/PhysRevLett.114.122501},

journal = {Physical Review Letters},

number = 12,

volume = 114,

place = {United States},

year = {Tue Mar 24 00:00:00 EDT 2015},

month = {Tue Mar 24 00:00:00 EDT 2015}

}