Bayesian approach to model-based extrapolation of nuclear observables

Neufcourt, Léo; Cao, Yuchen; Nazarewicz, Witold; Viens, Frederi

doi:10.1103/PhysRevC.98.034318

Title: Bayesian approach to model-based extrapolation of nuclear observables

Abstract

Here, we considered 10 global models based on nuclear density functional theory with realistic energy density functionals as well as two more phenomenological mass models. The emulators of two-neutron separation energy residuals and Bayesian confidence intervals defining theoretical error bars were constructed using Bayesian Gaussian processes and Bayesian neural networks. By establishing statistical methodology and parameters, we carried out extrapolations toward the two-neutron dripline. While both Gaussian processes (GP) and Bayesian neural networks reduce the root-mean-square (rms) deviation from experiment significantly, GP offers a better and much more stable performance. The increase in the predictive power of microscopic models aided by the statistical treatment is quite astonishing: The resulting rms deviations from experiment on the testing dataset are similar to those of more phenomenological models. The estimated credibility intervals on predictions make it possible to evaluate predictive power of individual models and also make quantified predictions using groups of models. The proposed robust statistical approach to extrapolation of nuclear model results can be useful for assessing the impact of current and future experiments in the context of model developments. The new Bayesian capability to evaluate residuals is also expected to impact research in the domains where experiments are currently impossible,more »« less

Authors:

Neufcourt, Léo ^[1]; Cao, Yuchen ^[1]; Nazarewicz, Witold ^[1]; Viens, Frederi ^[1]

Michigan State Univ., East Lansing, MI (United States)

Publication Date:: Mon Sep 24 00:00:00 EDT 2018

Research Org.:: Michigan State Univ., East Lansing, MI (United States)

Sponsoring Org.:: USDOE National Nuclear Security Administration (NNSA)

OSTI Identifier:: 1491246

Alternate Identifier(s):: OSTI ID: 1472205

Grant/Contract Number:: NA0002847; NA0002574; SC0018083; SC0013365

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review C

Additional Journal Information:: Journal Volume: 98; Journal Issue: 3; Journal ID: ISSN 2469-9985

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Citation Formats


                    Neufcourt, Léo, Cao, Yuchen, Nazarewicz, Witold, and Viens, Frederi. Bayesian approach to model-based extrapolation of nuclear observables.  United States: N. p., 2018. 
Web.  doi:10.1103/PhysRevC.98.034318.

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                    Neufcourt, Léo, Cao, Yuchen, Nazarewicz, Witold, & Viens, Frederi. Bayesian approach to model-based extrapolation of nuclear observables.  United States.  https://doi.org/10.1103/PhysRevC.98.034318

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                    Neufcourt, Léo, Cao, Yuchen, Nazarewicz, Witold, and Viens, Frederi. Mon .  
"Bayesian approach to model-based extrapolation of nuclear observables".  United States.  https://doi.org/10.1103/PhysRevC.98.034318.  https://www.osti.gov/servlets/purl/1491246.

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@article{osti_1491246,

  title        = {Bayesian approach to model-based extrapolation of nuclear observables},

  author       = {Neufcourt, Léo and Cao, Yuchen and Nazarewicz, Witold and Viens, Frederi},

  abstractNote = {Here, we considered 10 global models based on nuclear density functional theory with realistic energy density functionals as well as two more phenomenological mass models. The emulators of two-neutron separation energy residuals and Bayesian confidence intervals defining theoretical error bars were constructed using Bayesian Gaussian processes and Bayesian neural networks. By establishing statistical methodology and parameters, we carried out extrapolations toward the two-neutron dripline. While both Gaussian processes (GP) and Bayesian neural networks reduce the root-mean-square (rms) deviation from experiment significantly, GP offers a better and much more stable performance. The increase in the predictive power of microscopic models aided by the statistical treatment is quite astonishing: The resulting rms deviations from experiment on the testing dataset are similar to those of more phenomenological models. The estimated credibility intervals on predictions make it possible to evaluate predictive power of individual models and also make quantified predictions using groups of models. The proposed robust statistical approach to extrapolation of nuclear model results can be useful for assessing the impact of current and future experiments in the context of model developments. The new Bayesian capability to evaluate residuals is also expected to impact research in the domains where experiments are currently impossible, for instance, in simulations of the astrophysical r process.},

  doi          = {10.1103/PhysRevC.98.034318},

  journal      = {Physical Review C},

  number       = 3,

  volume       = 98,

  place        = {United States},

  year         = {Mon Sep 24 00:00:00 EDT 2018},

  month        = {Mon Sep 24 00:00:00 EDT 2018}

}

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Figures / Tables:

FIG. 1: The experimental $S$_2n($Z$;$N$) datasets for even-even nuclei used in our study: AME2003 (light dots, 537 points), additional data that appeared in the AME2016 evaluation (dark dots, 55 points), and JYFLTRAP (stars, 4 points).

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arXiv
DOI: 10.48550/arxiv.1901.07632

Electroweak probes of ground state densities
text, January 2019

Yang, Junjie; Hernandez, Jesse A.; Piekarewicz, J.
arXiv
DOI: 10.48550/arxiv.1908.10939

Beyond the proton drip line: Bayesian analysis of proton-emitting nuclei
text, January 2019

Neufcourt, Léo; Cao, Yuchen; Giuliani, Samuel
arXiv
DOI: 10.48550/arxiv.1910.12624

Impact of statistical uncertainties on the composition of the outer crust of a neutron star
text, January 2019

Pastore, A.; Neill, D.; Powell, H.
arXiv
DOI: 10.48550/arxiv.1912.11365

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The chart of the nuclides is limited by particle drip lines beyond which nuclear stability to proton or neutron emission is lost. Predicting the range of particle-bound isotopes poses an appreciable challenge for nuclear theory as it involves extreme extrapolations of nuclear masses well beyond the regions where experimental information is available. Still, quantified extrapolations are crucial for a wide variety of applications, including the modeling of stellar nucleosynthesis. We use microscopic nuclear global mass models, current mass data, and Bayesian methodology to provide quantified predictions of proton and neutron separation energies as well as Bayesian probabilities of existence throughoutmore »« less
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Similar Records

Title: Bayesian approach to model-based extrapolation of nuclear observables

Abstract

Citation Formats

Figures / Tables:

Nuclear mass predictions for the crustal composition of neutron stars: A Bayesian neural network approach journal, January 2016

New relativistic mean-field interaction with density-dependent meson-nucleon couplings journal, February 2005

Rates of convergence of the Hastings and Metropolis algorithms journal, February 1996

Uncertainties of mass extrapolations in Hartree-Fock-Bogoliubov mass models journal, May 2014

Microscopic mass formulas journal, July 1995

Probabilistic forecasts, calibration and sharpness journal, April 2007

Propagation of uncertainties in the nuclear DFT models journal, February 2015

The limits of the nuclear landscape journal, June 2012

Nuclear energy density optimization: Shell structure journal, May 2014

Hartree-Fock-Bogolyubov description of nuclei near the neutron-drip line journal, June 1984

Predictive power of nuclear-mass models journal, July 2014

Performance of the Levenberg–Marquardt neural network approach in nuclear mass prediction journal, March 2017

Relativistic mean-field interaction with density-dependent meson-nucleon vertices based on microscopical calculations journal, November 2011

David Draper and E. I. George, and a rejoinder by the authors journal, November 1999

The Ame2003 atomic mass evaluation journal, December 2003

The AME2016 atomic mass evaluation (II). Tables, graphs and references journal, March 2017

The Ame2003 atomic mass evaluation journal, December 2003

The AME2016 atomic mass evaluation (I). Evaluation of input data; and adjustment procedures journal, March 2017

A study on ground-state energies of nuclei by using neural networks journal, January 2014

Nuclear ground-state masses and deformations: FRDM(2012) journal, May 2016

Precision Mass Measurements on Neutron-Rich Rare-Earth Isotopes at JYFLTRAP: Reduced Neutron Pairing and Implications for r -Process Calculations journal, June 2018

Variations on a theme by Skyrme: A systematic study of adjustments of model parameters journal, March 2009

The effective force NL3 revisited journal, January 2009

Strictly Proper Scoring Rules, Prediction, and Estimation journal, March 2007

Estimating Parameter Uncertainty in Binding-Energy Models by the Frequency-Domain Bootstrap journal, December 2017

Global performance of covariant energy density functionals: Ground state observables of even-even nuclei and the estimate of theoretical uncertainties journal, May 2014

Towards a better parametrisation of Skyrme-like effective forces: A critical study of the SkM force journal, September 1982

Neutron drip line: Single-particle degrees of freedom and pairing properties as sources of theoretical uncertainties journal, January 2015

Uncertainty decomposition method and its application to the liquid drop model journal, March 2016

New Skyrme effective forces for supernovae and neutron rich nuclei journal, January 1995

Structure of even-even nuclei using a mapped collective Hamiltonian and the D1S Gogny interaction journal, January 2010

Positioning the neutron drip line and the r-process paths in the nuclear landscape journal, September 2015

Uncertainty propagation within the UNEDF models journal, March 2017

Global study of quadrupole correlation effects journal, March 2006

Valence p - n interactions and the development of collectivity in heavy nuclei journal, February 1987

Error estimates of theoretical models: a guide journal, May 2014

Nuclear mass predictions based on Bayesian neural network approach with pairing and shell effects journal, March 2018

Nuclear energy density optimization: Large deformations journal, February 2012

Uncertainty quantification and propagation in nuclear density functional theory journal, December 2015

Propagation of uncertainties in the Skyrme energy-density-functional model journal, March 2013

Refining mass formulas for astrophysical applications: A Bayesian neural network approach journal, October 2017

Addressing spectroscopic quality of covariant density functional theory journal, February 2015

Covariant energy density functionals: Nuclear matter constraints and global ground state properties journal, May 2016

Nuclidic Mass Formula on a Spherical Basis with an Improved Even-Odd Term journal, February 2005

On the Markov chain central limit theorem journal, January 2004

Bayesian calibration of computer models journal, August 2001

Nuclear energy density optimization journal, August 2010

Nuclear charge radii: density functional theory meets Bayesian neural networks journal, October 2016

The limits of the nuclear landscape explored by the relativistic continuum Hartree–Bogoliubov theory journal, May 2018

Self-consistent mean-field models for nuclear structure journal, January 2003

One-quasiparticle states in the nuclear energy density functional theory journal, February 2010

Validating neural-network refinements of nuclear mass models journal, January 2018

Relativistic nuclear energy density functionals: Adjusting parameters to binding energies journal, September 2008

Further explorations of Skyrme-Hartree-Fock-Bogoliubov mass formulas. XVI. Inclusion of self-energy effects in pairing journal, March 2016

Fluctuating parts of nuclear ground-state correlation energies journal, May 2013

The Ame2012 atomic mass evaluation journal, December 2012

Bayesian Model Selection and Model Averaging journal, March 2000

Nuclear mass systematics using neural networks journal, November 2004

Further explorations of Skyrme-Hartree-Fock-Bogoliubov mass formulas. XIII. The 2012 atomic mass evaluation and the symmetry coefficient journal, August 2013

Global microscopic calculations of ground-state spins and parities for odd-mass nuclei journal, August 2007

Optimizing relativistic energy density functionals: covariance analysis journal, February 2015

An approach to adjustment of relativistic mean field model parameters journal, January 2017

Uncertainty Quantification for Nuclear Density Functional Theory and Information Content of New Measurements journal, March 2015

Gamow-Hartree-Fock-Bogoliubov method: Representation of quasiparticles with Berggren sets of wave functions journal, October 2008

The Ame2012 atomic mass evaluation journal, December 2012

Towards a better parametrisation of Skyrme-like effective forces: A critical study of the SkM force text, January 1982

Markov Chain Monte Carlo in Practice journal, August 1997

Gamow-Hartree-Fock-Bogoliubov Method: Representation of quasiparticles with Berggren sets of wave functions text, January 2008

Relativistic Nuclear Energy Density Functionals: adjusting parameters to binding energies text, January 2008

The effective force NL3 revisited text, January 2009

One-quasiparticle States in the Nuclear Energy Density Functional Theory text, January 2009

Structure of even-even nuclei using a mapped collective Hamiltonian and the D1S Gogny interaction text, January 2009

Fluctuating parts of nuclear ground state correlation energies text, January 2012

Error Estimates of Theoretical Models: a Guide text, January 2014

Global performance of covariant energy density functionals: ground state observables of even-even nuclei and the estimate of theoretical uncertainties text, January 2014

Positioning the neutron drip line and the r-process paths in the nuclear landscape text, January 2014

Nuclear mass predictions for the crustal composition of neutron stars: A Bayesian neural network approach
journal, January 2016

New relativistic mean-field interaction with density-dependent meson-nucleon couplings
journal, February 2005

Rates of convergence of the Hastings and Metropolis algorithms
journal, February 1996

Uncertainties of mass extrapolations in Hartree-Fock-Bogoliubov mass models
journal, May 2014

Microscopic mass formulas
journal, July 1995

Probabilistic forecasts, calibration and sharpness
journal, April 2007

Propagation of uncertainties in the nuclear DFT models
journal, February 2015

The limits of the nuclear landscape
journal, June 2012

Nuclear energy density optimization: Shell structure
journal, May 2014

Hartree-Fock-Bogolyubov description of nuclei near the neutron-drip line
journal, June 1984

Predictive power of nuclear-mass models
journal, July 2014

Performance of the Levenberg–Marquardt neural network approach in nuclear mass prediction
journal, March 2017

Relativistic mean-field interaction with density-dependent meson-nucleon vertices based on microscopical calculations
journal, November 2011

David Draper and E. I. George, and a rejoinder by the authors
journal, November 1999

The Ame2003 atomic mass evaluation
journal, December 2003

The AME2016 atomic mass evaluation (II). Tables, graphs and references
journal, March 2017

The Ame2003 atomic mass evaluation
journal, December 2003

The AME2016 atomic mass evaluation (I). Evaluation of input data; and adjustment procedures
journal, March 2017

A study on ground-state energies of nuclei by using neural networks
journal, January 2014

Nuclear ground-state masses and deformations: FRDM(2012)
journal, May 2016

Precision Mass Measurements on Neutron-Rich Rare-Earth Isotopes at JYFLTRAP: Reduced Neutron Pairing and Implications for $r$ -Process Calculations
journal, June 2018

Variations on a theme by Skyrme: A systematic study of adjustments of model parameters
journal, March 2009

The effective force NL3 revisited
journal, January 2009

Strictly Proper Scoring Rules, Prediction, and Estimation
journal, March 2007

Estimating Parameter Uncertainty in Binding-Energy Models by the Frequency-Domain Bootstrap
journal, December 2017

Global performance of covariant energy density functionals: Ground state observables of even-even nuclei and the estimate of theoretical uncertainties
journal, May 2014

Towards a better parametrisation of Skyrme-like effective forces: A critical study of the SkM force
journal, September 1982

Neutron drip line: Single-particle degrees of freedom and pairing properties as sources of theoretical uncertainties
journal, January 2015

Uncertainty decomposition method and its application to the liquid drop model
journal, March 2016

New Skyrme effective forces for supernovae and neutron rich nuclei
journal, January 1995

Structure of even-even nuclei using a mapped collective Hamiltonian and the D1S Gogny interaction
journal, January 2010

Positioning the neutron drip line and the r-process paths in the nuclear landscape
journal, September 2015

Uncertainty propagation within the UNEDF models
journal, March 2017

Global study of quadrupole correlation effects
journal, March 2006

Valence p - n interactions and the development of collectivity in heavy nuclei
journal, February 1987

Error estimates of theoretical models: a guide
journal, May 2014

Nuclear mass predictions based on Bayesian neural network approach with pairing and shell effects
journal, March 2018

Nuclear energy density optimization: Large deformations
journal, February 2012

Uncertainty quantification and propagation in nuclear density functional theory
journal, December 2015

Propagation of uncertainties in the Skyrme energy-density-functional model
journal, March 2013

Refining mass formulas for astrophysical applications: A Bayesian neural network approach
journal, October 2017

Addressing spectroscopic quality of covariant density functional theory
journal, February 2015

Covariant energy density functionals: Nuclear matter constraints and global ground state properties
journal, May 2016

Nuclidic Mass Formula on a Spherical Basis with an Improved Even-Odd Term
journal, February 2005

On the Markov chain central limit theorem
journal, January 2004

Bayesian calibration of computer models
journal, August 2001

Nuclear energy density optimization
journal, August 2010

Nuclear charge radii: density functional theory meets Bayesian neural networks
journal, October 2016

The limits of the nuclear landscape explored by the relativistic continuum Hartree–Bogoliubov theory
journal, May 2018

Self-consistent mean-field models for nuclear structure
journal, January 2003

One-quasiparticle states in the nuclear energy density functional theory
journal, February 2010

Validating neural-network refinements of nuclear mass models
journal, January 2018

Relativistic nuclear energy density functionals: Adjusting parameters to binding energies
journal, September 2008

Further explorations of Skyrme-Hartree-Fock-Bogoliubov mass formulas. XVI. Inclusion of self-energy effects in pairing
journal, March 2016

Fluctuating parts of nuclear ground-state correlation energies
journal, May 2013

The Ame2012 atomic mass evaluation
journal, December 2012

Bayesian Model Selection and Model Averaging
journal, March 2000

Nuclear mass systematics using neural networks
journal, November 2004

Further explorations of Skyrme-Hartree-Fock-Bogoliubov mass formulas. XIII. The 2012 atomic mass evaluation and the symmetry coefficient
journal, August 2013

Global microscopic calculations of ground-state spins and parities for odd-mass nuclei
journal, August 2007

Optimizing relativistic energy density functionals: covariance analysis
journal, February 2015

An approach to adjustment of relativistic mean field model parameters
journal, January 2017

Uncertainty Quantification for Nuclear Density Functional Theory and Information Content of New Measurements
journal, March 2015

Gamow-Hartree-Fock-Bogoliubov method: Representation of quasiparticles with Berggren sets of wave functions
journal, October 2008

The Ame2012 atomic mass evaluation
journal, December 2012

Towards a better parametrisation of Skyrme-like effective forces: A critical study of the SkM force
text, January 1982

Markov Chain Monte Carlo in Practice
journal, August 1997

Gamow-Hartree-Fock-Bogoliubov Method: Representation of quasiparticles with Berggren sets of wave functions
text, January 2008

Relativistic Nuclear Energy Density Functionals: adjusting parameters to binding energies
text, January 2008

The effective force NL3 revisited
text, January 2009

One-quasiparticle States in the Nuclear Energy Density Functional Theory
text, January 2009

Structure of even-even nuclei using a mapped collective Hamiltonian and the D1S Gogny interaction
text, January 2009

Fluctuating parts of nuclear ground state correlation energies
text, January 2012

Error Estimates of Theoretical Models: a Guide
text, January 2014

Global performance of covariant energy density functionals: ground state observables of even-even nuclei and the estimate of theoretical uncertainties
text, January 2014

Positioning the neutron drip line and the r-process paths in the nuclear landscape
text, January 2014

Uncertainty Quantification for Nuclear Density Functional Theory and Information Content of New Measurements
text, January 2015

Covariant energy density functionals: nuclear matter constraints and global ground state properties
text, January 2016

Nuclear charge radii: Density functional theory meets Bayesian neural networks
text, January 2016

Uncertainty propagation within the UNEDF models
text, January 2016