Deep learning: Extrapolation tool for ab initio nuclear theory
Abstract
Ab initio approaches in nuclear theory, such as the nocore shell model (NCSM), have been developed for approximately solving finite nuclei with realistic strong interactions. The NCSM and other approaches require an extrapolation of the results obtained in a finite basis space to the infinite basis space limit and assessment of the uncertainty of those extrapolations. Each observable requires a separate extrapolation and many observables have no proven extrapolation method. Herein, we propose a feedforward artificial neural network (ANN) method as an extrapolation tool to obtain the groundstate energy and the groundstate pointproton rootmeansquare (rms) radius along with their extrapolation uncertainties. The designed ANNs are sufficient to produce results for these two very different observables in ^{6}Li from the ab initio NCSM results in small basis spaces that satisfy the following theoretical physics condition: independence of basis space parameters in the limit of extremely large matrices. Comparisons of the ANN findings with other extrapolation methods are also provided.
 Authors:

 Iowa State Univ., Ames, IA (United States); Horia Hulubei National Inst. for Physics and Nuclear Engineering, Bucharest (Romania)
 Iowa State Univ., Ames, IA (United States)
 Moscow State Univ. (Russia); Pacific National Univ. (Russia)
 Inst. of Basic Science, Daejeon (Korea, Republic of). Rare Isotope Science Project
 Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
 Publication Date:
 Research Org.:
 Iowa State Univ., Ames, IA (United States); Univ. of Tennessee, Knoxville, TN (United States); Univ. of California, Berkeley, CA (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Nuclear Physics (NP); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR). Scientific Discovery through Advanced Computing (SciDAC); Russian Science Foundation
 OSTI Identifier:
 1603455
 Alternate Identifier(s):
 OSTI ID: 1511892
 Grant/Contract Number:
 FG0287ER40371; SC0018223; AC0205CH11231; 2013M7A1A1075764
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Physical Review C
 Additional Journal Information:
 Journal Volume: 99; Journal Issue: 5; Journal ID: ISSN 24699985
 Publisher:
 American Physical Society (APS)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; Artificial Neural Networks; NoCore Shell Model; 6Li; ground state energy; root mean square radius; extrapolation
Citation Formats
Negoita, Gianina Alina, Vary, James P., Luecke, Glenn R., Maris, Pieter, Shirokov, Andrey M., Shin, Ik Jae, Kim, Youngman, Ng, Esmond G., Yang, Chao, Lockner, Matthew, and Prabhu, Gurpur M. Deep learning: Extrapolation tool for ab initio nuclear theory. United States: N. p., 2019.
Web. doi:10.1103/PhysRevC.99.054308.
Negoita, Gianina Alina, Vary, James P., Luecke, Glenn R., Maris, Pieter, Shirokov, Andrey M., Shin, Ik Jae, Kim, Youngman, Ng, Esmond G., Yang, Chao, Lockner, Matthew, & Prabhu, Gurpur M. Deep learning: Extrapolation tool for ab initio nuclear theory. United States. doi:10.1103/PhysRevC.99.054308.
Negoita, Gianina Alina, Vary, James P., Luecke, Glenn R., Maris, Pieter, Shirokov, Andrey M., Shin, Ik Jae, Kim, Youngman, Ng, Esmond G., Yang, Chao, Lockner, Matthew, and Prabhu, Gurpur M. Fri .
"Deep learning: Extrapolation tool for ab initio nuclear theory". United States. doi:10.1103/PhysRevC.99.054308. https://www.osti.gov/servlets/purl/1603455.
@article{osti_1603455,
title = {Deep learning: Extrapolation tool for ab initio nuclear theory},
author = {Negoita, Gianina Alina and Vary, James P. and Luecke, Glenn R. and Maris, Pieter and Shirokov, Andrey M. and Shin, Ik Jae and Kim, Youngman and Ng, Esmond G. and Yang, Chao and Lockner, Matthew and Prabhu, Gurpur M.},
abstractNote = {Ab initio approaches in nuclear theory, such as the nocore shell model (NCSM), have been developed for approximately solving finite nuclei with realistic strong interactions. The NCSM and other approaches require an extrapolation of the results obtained in a finite basis space to the infinite basis space limit and assessment of the uncertainty of those extrapolations. Each observable requires a separate extrapolation and many observables have no proven extrapolation method. Herein, we propose a feedforward artificial neural network (ANN) method as an extrapolation tool to obtain the groundstate energy and the groundstate pointproton rootmeansquare (rms) radius along with their extrapolation uncertainties. The designed ANNs are sufficient to produce results for these two very different observables in 6Li from the ab initio NCSM results in small basis spaces that satisfy the following theoretical physics condition: independence of basis space parameters in the limit of extremely large matrices. Comparisons of the ANN findings with other extrapolation methods are also provided.},
doi = {10.1103/PhysRevC.99.054308},
journal = {Physical Review C},
number = 5,
volume = 99,
place = {United States},
year = {2019},
month = {5}
}
Web of Science
Works referenced in this record:
Ab initio no core shell model
journal, March 2013
 Barrett, Bruce R.; Navrátil, Petr; Vary, James P.
 Progress in Particle and Nuclear Physics, Vol. 69
Ab initio nuclear structure – the large sparse matrix eigenvalue problem
journal, July 2009
 Vary, James P.; Maris, Pieter; Ng, Esmond
 Journal of Physics: Conference Series, Vol. 180
Ab initio nocore full configuration calculations of light nuclei
journal, January 2009
 Maris, P.; Vary, J. P.; Shirokov, A. M.
 Physical Review C, Vol. 79, Issue 1
AB INITIO NUCLEAR STRUCTURE CALCULATIONS OF pSHELL NUCLEI WITH JISP16
journal, July 2013
 Maris, Pieter; Vary, James P.
 International Journal of Modern Physics E, Vol. 22, Issue 07
Ab initio nocore solutions for ^{6} Li
journal, May 2017
 Shin, Ik Jae; Kim, Youngman; Maris, Pieter
 Journal of Physics G: Nuclear and Particle Physics, Vol. 44, Issue 7
Impact parameter determination for heavyion collisions by use of a neural network
journal, March 1995
 David, Christophe; Freslier, Marc; Aichelin, Jörg
 Physical Review C, Vol. 51, Issue 3
Neural networks for impact parameter determination
journal, May 1996
 Bass, S. A.; Bischoff, A.; Maruhn, J. A.
 Physical Review C, Vol. 53, Issue 5
Impact parameter determination in experimental analysis using a neural network
journal, March 1997
 Haddad, F.; Hagel, K.; Li, J.
 Physical Review C, Vol. 55, Issue 3
Nuclear mass systematics using neural networks
journal, November 2004
 Athanassopoulos, S.; Mavrommatis, E.; Gernoth, K. A.
 Nuclear Physics A, Vol. 743, Issue 4
Decoding $\beta $ decay systematics: A global statistical model for ${\beta}^{}$ halflives
journal, October 2009
 Costiris, N. J.; Mavrommatis, E.; Gernoth, K. A.
 Physical Review C, Vol. 80, Issue 4
An artificial neural network application on nuclear charge radii
journal, March 2013
 Akkoyun, S.; Bayram, T.; Kara, S. O.
 Journal of Physics G: Nuclear and Particle Physics, Vol. 40, Issue 5
Consistent empirical physical formulas for potential energy curves of 38–66Ti isotopes by using neural networks
journal, November 2013
 Akkoyun, S.; Bayram, T.; Kara, S. O.
 Physics of Particles and Nuclei Letters, Vol. 10, Issue 6
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
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
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
Validating neuralnetwork refinements of nuclear mass models
journal, January 2018
 Utama, R.; Piekarewicz, J.
 Physical Review C, Vol. 97, Issue 1
Bayesian approach to modelbased extrapolation of nuclear observables
journal, September 2018
 Neufcourt, Léo; Cao, Yuchen; Nazarewicz, Witold
 Physical Review C, Vol. 98, Issue 3
Scaling of abinitio nuclear physics calculations on multicore computer architectures
journal, May 2010
 Maris, Pieter; Sosonkina, Masha; Vary, James P.
 Procedia Computer Science, Vol. 1, Issue 1
Improving the scalability of a symmetric iterative eigensolver for multicore platforms: IMPROVING THE SCALABILITY OF A SYMMETRIC ITERATIVE EIGENSOLVER
journal, September 2013
 Aktulga, Hasan Metin; Yang, Chao; Ng, Esmond G.
 Concurrency and Computation: Practice and Experience, Vol. 26, Issue 16
N3LO NN interaction adjusted to light nuclei in ab exitu approach
journal, October 2016
 Shirokov, A. M.; Shin, I. J.; Kim, Y.
 Physics Letters B, Vol. 761
Largescale exact diagonalizations reveal lowmomentum scales of nuclei
journal, March 2018
 Forssén, C.; Carlsson, B. D.; Johansson, H. T.
 Physical Review C, Vol. 97, Issue 3
Accurate nucleon–nucleon potential based upon chiral perturbation theory
journal, January 2002
 Entem, D. R.; Machleidt, R.
 Physics Letters B, Vol. 524, Issue 12
Accurate chargedependent nucleonnucleon potential at fourth order of chiral perturbation theory
journal, October 2003
 Entem, D. R.; Machleidt, R.
 Physical Review C, Vol. 68, Issue 4
Similarity renormalization group for nucleonnucleon interactions
journal, June 2007
 Bogner, S. K.; Furnstahl, R. J.; Perry, R. J.
 Physical Review C, Vol. 75, Issue 6
From lowmomentum interactions to nuclear structure
journal, July 2010
 Bogner, S. K.; Furnstahl, R. J.; Schwenk, A.
 Progress in Particle and Nuclear Physics, Vol. 65, Issue 1
Loosely bound threebody nuclear systems in the Jmatrix approach
journal, August 2004
 Lurie, Yu. A.; Shirokov, A. M.
 Annals of Physics, Vol. 312, Issue 2
Nucleonnucleon interaction in the $J$ matrix inverse scattering approach and fewnucleon systems
journal, October 2004
 Shirokov, A. M.; Mazur, A. I.; Zaytsev, S. A.
 Physical Review C, Vol. 70, Issue 4
CoulombSturmian basis for the nuclear manybody problem
journal, September 2012
 Caprio, M. A.; Maris, P.; Vary, J. P.
 Physical Review C, Vol. 86, Issue 3
Halo nuclei ${}^{6}\mathrm{He}$ and ${}^{8}\mathrm{He}$ with the CoulombSturmian basis
journal, September 2014
 Caprio, M. A.; Maris, P.; Vary, J. P.
 Physical Review C, Vol. 90, Issue 3
Natural orbital description of the halo nucleus 6He
journal, November 2017
 Constantinou, Chrysovalantis; Caprio, Mark A.; Vary, James P.
 Nuclear Science and Techniques, Vol. 28, Issue 12
CenterofMass Motion in Brueckner Theory for a Finite Nucleus
journal, March 1958
 Lipkin, Harry J.
 Physical Review, Vol. 109, Issue 6
Spurious centerofmass motion
journal, December 1974
 Gloeckner, D. H.; Lawson, R. D.
 Physics Letters B, Vol. 53, Issue 4
Convergence properties of ab initio calculations of light nuclei in a harmonic oscillator basis
journal, November 2012
 Coon, S. A.; Avetian, M. I.; Kruse, M. K. G.
 Physical Review C, Vol. 86, Issue 5
Corrections to nuclear energies and radii in finite oscillator spaces
journal, September 2012
 Furnstahl, R. J.; Hagen, G.; Papenbrock, T.
 Physical Review C, Vol. 86, Issue 3
Universal properties of infrared oscillator basis extrapolations
journal, April 2013
 More, S. N.; Ekström, A.; Furnstahl, R. J.
 Physical Review C, Vol. 87, Issue 4
Infrared length scale and extrapolations for the nocore shell model
journal, June 2015
 Wendt, K. A.; Forssén, C.; Papenbrock, T.
 Physical Review C, Vol. 91, Issue 6
Infrared extrapolations of quadrupole moments and transitions
journal, April 2016
 Odell, D.; Papenbrock, T.; Platter, L.
 Physical Review C, Vol. 93, Issue 4
Corrections to nucleon capture cross sections computed in truncated Hilbert spaces
journal, March 2017
 Acharya, B.; Ekström, A.; Odell, D.
 Physical Review C, Vol. 95, Issue 3
Multilayer feedforward networks are universal approximators
journal, January 1989
 Hornik, Kurt; Stinchcombe, Maxwell; White, Halbert
 Neural Networks, Vol. 2, Issue 5
Training feedforward networks with the Marquardt algorithm
journal, January 1994
 Hagan, M. T.; Menhaj, M. B.
 IEEE Transactions on Neural Networks, Vol. 5, Issue 6
An Algorithm for LeastSquares Estimation of Nonlinear Parameters
journal, June 1963
 Marquardt, Donald W.
 Journal of the Society for Industrial and Applied Mathematics, Vol. 11, Issue 2
Approximation by superpositions of a sigmoidal function
journal, December 1989
 Cybenko, G.
 Mathematics of Control, Signals, and Systems, Vol. 2, Issue 4
Covariant spectator theory of $\mathit{np}$ scattering: Phase shifts obtained from precision fits to data below 350 MeV
journal, July 2008
 Gross, Franz; Stadler, Alfred
 Physical Review C, Vol. 78, Issue 1
Erratum: Coarsegrained potential analysis of neutronproton and protonproton scattering below the pion production threshold [Phys. Rev. C 88 , 064002 (2013)]
journal, February 2015
 Navarro Pérez, R.; Amaro, J. E.; Arriola, E. Ruiz
 Physical Review C, Vol. 91, Issue 2
Energy levels of light nuclei A=5, 6, 7
journal, September 2002
 Tilley, D. R.; Cheves, C. M.; Godwin, J. L.
 Nuclear Physics A, Vol. 708, Issue 12
Recent experimental progress in nuclear halo structure studies
journal, January 2013
 Tanihata, Isao; Savajols, Herve; Kanungo, Rituparna
 Progress in Particle and Nuclear Physics, Vol. 68
Works referencing / citing this record:
Extrapolation of nuclear structure observables with artificial neural networks
journal, November 2019
 Jiang, W. G.; Hagen, G.; Papenbrock, T.
 Physical Review C, Vol. 100, Issue 5
Predictions of nuclear charge radii and physical interpretations based on the naive Bayesian probability classifier
journal, January 2020
 Ma, Yunfei; Su, Chen; Liu, Jian
 Physical Review C, Vol. 101, Issue 1