Bayesian approach to modelbased 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 twoneutron 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 twoneutron dripline. While both Gaussian processes (GP) and Bayesian neural networks reduce the rootmeansquare (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 »
 Authors:

 Michigan State Univ., East Lansing, MI (United States)
 Publication Date:
 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 24699985
 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 modelbased extrapolation of nuclear observables. United States: N. p., 2018.
Web. doi:10.1103/PhysRevC.98.034318.
Neufcourt, Léo, Cao, Yuchen, Nazarewicz, Witold, & Viens, Frederi. Bayesian approach to modelbased extrapolation of nuclear observables. United States. https://doi.org/10.1103/PhysRevC.98.034318
Neufcourt, Léo, Cao, Yuchen, Nazarewicz, Witold, and Viens, Frederi. Mon .
"Bayesian approach to modelbased extrapolation of nuclear observables". United States. https://doi.org/10.1103/PhysRevC.98.034318. https://www.osti.gov/servlets/purl/1491246.
@article{osti_1491246,
title = {Bayesian approach to modelbased 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 twoneutron 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 twoneutron dripline. While both Gaussian processes (GP) and Bayesian neural networks reduce the rootmeansquare (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 = {2018},
month = {9}
}
Web of Science
Figures / Tables:
Works referenced in this record:
Nuclear mass predictions for the crustal composition of neutron stars: A Bayesian neural network approach
journal, January 2016
 Utama, R.; Piekarewicz, J.; Prosper, H. B.
 Physical Review C, Vol. 93, Issue 1
New relativistic meanfield interaction with densitydependent mesonnucleon couplings
journal, February 2005
 Lalazissis, G. A.; Nikšić, T.; Vretenar, D.
 Physical Review C, Vol. 71, Issue 2
Rates of convergence of the Hastings and Metropolis algorithms
journal, February 1996
 Mengersen, K. L.; Tweedie, R. L.
 The Annals of Statistics, Vol. 24, Issue 1
Uncertainties of mass extrapolations in HartreeFockBogoliubov mass models
journal, May 2014
 Goriely, S.; Capote, R.
 Physical Review C, Vol. 89, Issue 5
Microscopic mass formulas
journal, July 1995
 Duflo, J.; Zuker, A. P.
 Physical Review C, Vol. 52, Issue 1
Probabilistic forecasts, calibration and sharpness
journal, April 2007
 Gneiting, Tilmann; Balabdaoui, Fadoua; Raftery, Adrian E.
 Journal of the Royal Statistical Society: Series B (Statistical Methodology), Vol. 69, Issue 2
Propagation of uncertainties in the nuclear DFT models
journal, February 2015
 Kortelainen, Markus
 Journal of Physics G: Nuclear and Particle Physics, Vol. 42, Issue 3
The limits of the nuclear landscape
journal, June 2012
 Erler, Jochen; Birge, Noah; Kortelainen, Markus
 Nature, Vol. 486, Issue 7404
Nuclear energy density optimization: Shell structure
journal, May 2014
 Kortelainen, M.; McDonnell, J.; Nazarewicz, W.
 Physical Review C, Vol. 89, Issue 5
HartreeFockBogolyubov description of nuclei near the neutrondrip line
journal, June 1984
 Dobaczewski, J.; Flocard, H.; Treiner, J.
 Nuclear Physics A, Vol. 422, Issue 1
Predictive power of nuclearmass models
journal, July 2014
 Sobiczewski, Adam; Litvinov, Yuri A.
 Physical Review C, Vol. 90, Issue 1
Performance of the Levenberg–Marquardt neural network approach in nuclear mass prediction
journal, March 2017
 Zhang, Hai Fei; Wang, Li Hao; Yin, Jing Peng
 Journal of Physics G: Nuclear and Particle Physics, Vol. 44, Issue 4
Relativistic meanfield interaction with densitydependent mesonnucleon vertices based on microscopical calculations
journal, November 2011
 RocaMaza, X.; Viñas, X.; Centelles, M.
 Physical Review C, Vol. 84, Issue 5
David Draper and E. I. George, and a rejoinder by the authors
journal, November 1999
 Volinsky, Chris T.; Raftery, Adrian E.; Madigan, David
 Statistical Science, Vol. 14, Issue 4
The Ame2003 atomic mass evaluation
journal, December 2003
 Wapstra, A. H.; Audi, G.; Thibault, C.
 Nuclear Physics A, Vol. 729, Issue 1
The AME2016 atomic mass evaluation (II). Tables, graphs and references
journal, March 2017
 Wang, Meng; Audi, G.; Kondev, F. G.
 Chinese Physics C, Vol. 41, Issue 3
The Ame2003 atomic mass evaluation
journal, December 2003
 Audi, G.; Wapstra, A. H.; Thibault, C.
 Nuclear Physics A, Vol. 729, Issue 1
The AME2016 atomic mass evaluation (I). Evaluation of input data; and adjustment procedures
journal, March 2017
 Huang, W. J.; Audi, G.; Wang, Meng
 Chinese Physics C, Vol. 41, Issue 3
A study on groundstate energies of nuclei by using neural networks
journal, January 2014
 Bayram, Tuncay; Akkoyun, Serkan; Kara, S. Okan
 Annals of Nuclear Energy, Vol. 63
Nuclear groundstate masses and deformations: FRDM(2012)
journal, May 2016
 Möller, P.; Sierk, A. J.; Ichikawa, T.
 Atomic Data and Nuclear Data Tables, Vol. 109110
Precision Mass Measurements on NeutronRich RareEarth Isotopes at JYFLTRAP: Reduced Neutron Pairing and Implications for $r$ Process Calculations
journal, June 2018
 Vilen, M.; Kelly, J. M.; Kankainen, A.
 Physical Review Letters, Vol. 120, Issue 26
Variations on a theme by Skyrme: A systematic study of adjustments of model parameters
journal, March 2009
 Klüpfel, P.; Reinhard, P. G.; Bürvenich, T. J.
 Physical Review C, Vol. 79, Issue 3
The effective force NL3 revisited
journal, January 2009
 Lalazissis, G. A.; Karatzikos, S.; Fossion, R.
 Physics Letters B, Vol. 671, Issue 1
Strictly Proper Scoring Rules, Prediction, and Estimation
journal, March 2007
 Gneiting, Tilmann; Raftery, Adrian E.
 Journal of the American Statistical Association, Vol. 102, Issue 477
Estimating Parameter Uncertainty in BindingEnergy Models by the FrequencyDomain Bootstrap
journal, December 2017
 Bertsch, G. F.; Bingham, Derek
 Physical Review Letters, Vol. 119, Issue 25
Global performance of covariant energy density functionals: Ground state observables of eveneven nuclei and the estimate of theoretical uncertainties
journal, May 2014
 Agbemava, S. E.; Afanasjev, A. V.; Ray, D.
 Physical Review C, Vol. 89, Issue 5
Towards a better parametrisation of Skyrmelike effective forces: A critical study of the SkM force
journal, September 1982
 Bartel, J.; Quentin, P.; Brack, M.
 Nuclear Physics A, Vol. 386, Issue 1
Neutron drip line: Singleparticle degrees of freedom and pairing properties as sources of theoretical uncertainties
journal, January 2015
 Afanasjev, A. V.; Agbemava, S. E.; Ray, D.
 Physical Review C, Vol. 91, Issue 1
Uncertainty decomposition method and its application to the liquid drop model
journal, March 2016
 Yuan, Cenxi
 Physical Review C, Vol. 93, Issue 3
New Skyrme effective forces for supernovae and neutron rich nuclei
journal, January 1995
 Chabanat, E.; Bonche, P.; Haensel, P.
 Physica Scripta, Vol. T56
Structure of eveneven nuclei using a mapped collective Hamiltonian and the D1S Gogny interaction
journal, January 2010
 Delaroche, J. P.; Girod, M.; Libert, J.
 Physical Review C, Vol. 81, Issue 1
Positioning the neutron drip line and the rprocess paths in the nuclear landscape
journal, September 2015
 Wang, Rui; Chen, LieWen
 Physical Review C, Vol. 92, Issue 3
Uncertainty propagation within the UNEDF models
journal, March 2017
 Haverinen, T.; Kortelainen, M.
 Journal of Physics G: Nuclear and Particle Physics, Vol. 44, Issue 4
Global study of quadrupole correlation effects
journal, March 2006
 Bender, M.; Bertsch, G. F.; Heenen, P. H.
 Physical Review C, Vol. 73, Issue 3
Valence p  n interactions and the development of collectivity in heavy nuclei
journal, February 1987
 Casten, R. F.; Brenner, D. S.; Haustein, P. E.
 Physical Review Letters, Vol. 58, Issue 7
Error estimates of theoretical models: a guide
journal, May 2014
 Dobaczewski, J.; Nazarewicz, W.; Reinhard, PG
 Journal of Physics G: Nuclear and Particle Physics, Vol. 41, Issue 7
Nuclear mass predictions based on Bayesian neural network approach with pairing and shell effects
journal, March 2018
 Niu, Z. M.; Liang, H. Z.
 Physics Letters B, Vol. 778
Nuclear energy density optimization: Large deformations
journal, February 2012
 Kortelainen, M.; McDonnell, J.; Nazarewicz, W.
 Physical Review C, Vol. 85, Issue 2
Uncertainty quantification and propagation in nuclear density functional theory
journal, December 2015
 Schunck, N.; McDonnell, J. D.; Higdon, D.
 The European Physical Journal A, Vol. 51, Issue 12
Propagation of uncertainties in the Skyrme energydensityfunctional model
journal, March 2013
 Gao, Y.; Dobaczewski, J.; Kortelainen, M.
 Physical Review C, Vol. 87, Issue 3
Refining mass formulas for astrophysical applications: A Bayesian neural network approach
journal, October 2017
 Utama, R.; Piekarewicz, J.
 Physical Review C, Vol. 96, Issue 4
Addressing spectroscopic quality of covariant density functional theory
journal, February 2015
 Afanasjev, A. V.
 Journal of Physics G: Nuclear and Particle Physics, Vol. 42, Issue 3
Covariant energy density functionals: Nuclear matter constraints and global ground state properties
journal, May 2016
 Afanasjev, A. V.; Agbemava, S. E.
 Physical Review C, Vol. 93, Issue 5
Nuclidic Mass Formula on a Spherical Basis with an Improved EvenOdd Term
journal, February 2005
 Koura, H.; Tachibana, T.; Uno, M.
 Progress of Theoretical Physics, Vol. 113, Issue 2
On the Markov chain central limit theorem
journal, January 2004
 Jones, Galin L.
 Probability Surveys, Vol. 1, Issue 0
Bayesian Learning for Neural Networks
book, January 1996
 Neal, Radford M.
 Lecture Notes in Statistics
Bayesian calibration of computer models
journal, August 2001
 Kennedy, Marc C.; O'Hagan, Anthony
 Journal of the Royal Statistical Society: Series B (Statistical Methodology), Vol. 63, Issue 3
Nuclear energy density optimization
journal, August 2010
 Kortelainen, M.; Lesinski, T.; Moré, J.
 Physical Review C, Vol. 82, Issue 2
Nuclear charge radii: density functional theory meets Bayesian neural networks
journal, October 2016
 Utama, R.; Chen, WeiChia; Piekarewicz, J.
 Journal of Physics G: Nuclear and Particle Physics, Vol. 43, Issue 11
The limits of the nuclear landscape explored by the relativistic continuum Hartree–Bogoliubov theory
journal, May 2018
 Xia, X. W.; Lim, Y.; Zhao, P. W.
 Atomic Data and Nuclear Data Tables, Vol. 121122
Selfconsistent meanfield models for nuclear structure
journal, January 2003
 Bender, Michael; Heenen, PaulHenri; Reinhard, PaulGerhard
 Reviews of Modern Physics, Vol. 75, Issue 1
Onequasiparticle states in the nuclear energy density functional theory
journal, February 2010
 Schunck, N.; Dobaczewski, J.; McDonnell, J.
 Physical Review C, Vol. 81, Issue 2
Markov Chain Monte Carlo in Practice
book, December 1995
 Gilks, W. R.; Richardson, S.; Spiegelhalter, David
 Chapman and Hall/CRC
Validating neuralnetwork refinements of nuclear mass models
journal, January 2018
 Utama, R.; Piekarewicz, J.
 Physical Review C, Vol. 97, Issue 1
Relativistic nuclear energy density functionals: Adjusting parameters to binding energies
journal, September 2008
 Nikšić, T.; Vretenar, D.; Ring, P.
 Physical Review C, Vol. 78, Issue 3
Further explorations of SkyrmeHartreeFockBogoliubov mass formulas. XVI. Inclusion of selfenergy effects in pairing
journal, March 2016
 Goriely, S.; Chamel, N.; Pearson, J. M.
 Physical Review C, Vol. 93, Issue 3
Fluctuating parts of nuclear groundstate correlation energies
journal, May 2013
 Carlsson, B. G.; Toivanen, J.; von Barth, U.
 Physical Review C, Vol. 87, Issue 5
The Ame2012 atomic mass evaluation
journal, December 2012
 Wang, M.; Audi, G.; Wapstra, A. H.
 Chinese Physics C, Vol. 36, Issue 12
Bayesian Model Selection and Model Averaging
journal, March 2000
 Wasserman, Larry
 Journal of Mathematical Psychology, Vol. 44, Issue 1
Nuclear mass systematics using neural networks
journal, November 2004
 Athanassopoulos, S.; Mavrommatis, E.; Gernoth, K. A.
 Nuclear Physics A, Vol. 743, Issue 4
Further explorations of SkyrmeHartreeFockBogoliubov mass formulas. XIII. The 2012 atomic mass evaluation and the symmetry coefficient
journal, August 2013
 Goriely, S.; Chamel, N.; Pearson, J. M.
 Physical Review C, Vol. 88, Issue 2
Global microscopic calculations of groundstate spins and parities for oddmass nuclei
journal, August 2007
 Bonneau, L.; Quentin, P.; Möller, P.
 Physical Review C, Vol. 76, Issue 2
Optimizing relativistic energy density functionals: covariance analysis
journal, February 2015
 Nikšić, T.; Paar, N.; Reinhard, PG
 Journal of Physics G: Nuclear and Particle Physics, Vol. 42, Issue 3
An approach to adjustment of relativistic mean field model parameters
journal, January 2017
 Bayram, Tuncay; Akkoyun, Serkan
 EPJ Web of Conferences, Vol. 146
Uncertainty Quantification for Nuclear Density Functional Theory and Information Content of New Measurements
journal, March 2015
 McDonnell, J. D.; Schunck, N.; Higdon, D.
 Physical Review Letters, Vol. 114, Issue 12
GamowHartreeFockBogoliubov method: Representation of quasiparticles with Berggren sets of wave functions
journal, October 2008
 Michel, N.; Matsuyanagi, K.; Stoitsov, M.
 Physical Review C, Vol. 78, Issue 4
The Ame2012 atomic mass evaluation
journal, December 2012
 Audi, G.; Wang, M.; Wapstra, A. H.
 Chinese Physics C, Vol. 36, Issue 12
Towards a better parametrisation of Skyrmelike effective forces: A critical study of the SkM force
text, January 1982
 Bartel, J.; Quentin, P.; Brack, Matthias
 Universität Regensburg
Markov Chain Monte Carlo in Practice
journal, August 1997
 Gasparini, Mauro
 Technometrics, Vol. 39, Issue 3
GamowHartreeFockBogoliubov Method: Representation of quasiparticles with Berggren sets of wave functions
text, January 2008
 Michel, N.; Matsuyanagi, K.; Stoitsov, M.
 arXiv
Relativistic Nuclear Energy Density Functionals: adjusting parameters to binding energies
text, January 2008
 Niksic, T.; Vretenar, D.; Ring, P.
 arXiv
The effective force NL3 revisited
text, January 2009
 Lalazissis, G. A.; Karatzikos, S.; Fossion, R.
 arXiv
Onequasiparticle States in the Nuclear Energy Density Functional Theory
text, January 2009
 Schunck, N.; Dobaczewski, J.; McDonnell, J.
 arXiv
Structure of eveneven nuclei using a mapped collective Hamiltonian and the D1S Gogny interaction
text, January 2009
 Delaroche, J. P.; Girod, M.; Libert, J.
 arXiv
Fluctuating parts of nuclear ground state correlation energies
text, January 2012
 Carlsson, B. G.; Toivanen, J.; von Barth, U.
 arXiv
Error Estimates of Theoretical Models: a Guide
text, January 2014
 Dobaczewski, J.; Nazarewicz, W.; Reinhard, P. G.
 arXiv
Global performance of covariant energy density functionals: ground state observables of eveneven nuclei and the estimate of theoretical uncertainties
text, January 2014
 Agbemava, S. E.; Afanasjev, A. V.; Ray, D.
 arXiv
Positioning the neutron drip line and the rprocess paths in the nuclear landscape
text, January 2014
 Wang, Rui; Chen, LieWen
 arXiv
Uncertainty Quantification for Nuclear Density Functional Theory and Information Content of New Measurements
text, January 2015
 McDonnell, J. D.; Schunck, N.; Higdon, D.
 arXiv
Covariant energy density functionals: nuclear matter constraints and global ground state properties
text, January 2016
 Afanasjev, A. V.; Agbemava, S. E.
 arXiv
Nuclear charge radii: Density functional theory meets Bayesian neural networks
text, January 2016
 Utama, Raditya; Chen, WeiChia; Piekarewicz, Jorge
 arXiv
Uncertainty propagation within the UNEDF models
text, January 2016
 Haverinen, T.; Kortelainen, M.
 arXiv
Refining mass formulas for astrophysical applications: a Bayesian neural network approach
text, January 2017
 Utama, Raditya; Piekarewicz, Jorge
 arXiv
The limits of the nuclear landscape explored by the relativistic continuum HatreeBogoliubov theory
text, January 2017
 Xia, X. W.; Lim, Y.; Zhao, P. W.
 arXiv
Validating neuralnetwork refinements of nuclear mass models
text, January 2017
 Utama, R.; Piekarewicz, J.
 arXiv
Nuclear mass predictions based on Bayesian neural network approach with pairing and shell effects
text, January 2018
 Niu, Z. M.; Liang, H. Z.
 arXiv
Precision mass measurements on neutronrich rareearth isotopes at JYFLTRAP  reduced neutron pairing and implications for the $r$process calculations
text, January 2018
 Vilen, M.; Kelly, J. M.; Kankainen, A.
 arXiv
Global study of quadrupole correlation effects
text, January 2005
 Bender, M.; Bertsch, G. F.; Heenen, P. H.
 arXiv
Global microscopic calculations of groundstate spin and parity for oddmass nuclei
text, January 2007
 Bonneau, Ludovic; Quentin, Philippe; Moller, Peter
 arXiv
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text, January 2018
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