Deep learning: Extrapolation tool for ab initio nuclear theory

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.

doi:10.1103/PhysRevC.99.054308

Title: Deep learning: Extrapolation tool for ab initio nuclear theory

Journal Article · Fri May 10 00:00:00 EDT 2019 · Physical Review C

DOI:https://doi.org/10.1103/PhysRevC.99.054308· OSTI ID:1603455

Negoita, Gianina Alina ^[1];

^[2]; Luecke, Glenn R. ^[2]; Maris, Pieter ^[2]; Shirokov, Andrey M. ^[3]; Shin, Ik Jae ^[4]; Kim, Youngman ^[4]; Ng, Esmond G. ^[5]; Yang, Chao ^[5]; Lockner, Matthew ^[2]; Prabhu, Gurpur M. ^[2]

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)

Ab initio approaches in nuclear theory, such as the no-core 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 feed-forward artificial neural network (ANN) method as an extrapolation tool to obtain the ground-state energy and the ground-state point-proton root-mean-square (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.

View Accepted Manuscript (DOE)

View Accepted Manuscript (Publisher)

Cite

Export

Save

Research Organization:: Iowa State Univ., Ames, IA (United States); Univ. of Tennessee, Knoxville, TN (United States); University of California, Berkeley, CA (United States)

Sponsoring Organization:: 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

Grant/Contract Number:: FG02-87ER40371; SC0018223; AC02-05CH11231; 2013M7A1A1075764

OSTI ID:: 1603455

Alternate ID(s):: OSTI ID: 1511892

Journal Information:: Physical Review C, Vol. 99, Issue 5; ISSN 2469-9985

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 35 works

Citation information provided by
Web of Science

References (68)

Nuclear mass predictions for the crustal composition of neutron stars: A Bayesian neural network approach Utama, R.; Piekarewicz, J.; Prosper, H. B. Physical Review C, Vol. 93, Issue 1 https://doi.org/10.1103/PhysRevC.93.014311	journal	January 2016
Large-scale exact diagonalizations reveal low-momentum scales of nuclei Forssén, C.; Carlsson, B. D.; Johansson, H. T. Physical Review C, Vol. 97, Issue 3 https://doi.org/10.1103/PhysRevC.97.034328	journal	March 2018
Ab initio no core shell model Barrett, Bruce R.; Navrátil, Petr; Vary, James P. Progress in Particle and Nuclear Physics, Vol. 69 https://doi.org/10.1016/j.ppnp.2012.10.003	journal	March 2013
Nucleon-nucleon interaction in the $J$ -matrix inverse scattering approach and few-nucleon systems Shirokov, A. M.; Mazur, A. I.; Zaytsev, S. A. Physical Review C, Vol. 70, Issue 4 https://doi.org/10.1103/PhysRevC.70.044005	journal	October 2004
Consistent empirical physical formulas for potential energy curves of 38–66Ti isotopes by using neural networks Akkoyun, S.; Bayram, T.; Kara, S. O. Physics of Particles and Nuclei Letters, Vol. 10, Issue 6 https://doi.org/10.1134/S1547477113060022	journal	November 2013
Spurious center-of-mass motion Gloeckner, D. H.; Lawson, R. D. Physics Letters B, Vol. 53, Issue 4 https://doi.org/10.1016/0370-2693(74)90390-6	journal	December 1974
Neural networks for impact parameter determination Bass, S. A.; Bischoff, A.; Maruhn, J. A. Physical Review C, Vol. 53, Issue 5 https://doi.org/10.1103/PhysRevC.53.2358	journal	May 1996
Scaling of ab-initio nuclear physics calculations on multicore computer architectures Maris, Pieter; Sosonkina, Masha; Vary, James P. Procedia Computer Science, Vol. 1, Issue 1 https://doi.org/10.1016/j.procs.2010.04.012	journal	May 2010
Energy levels of light nuclei A=5, 6, 7 Tilley, D. R.; Cheves, C. M.; Godwin, J. L. Nuclear Physics A, Vol. 708, Issue 1-2 https://doi.org/10.1016/S0375-9474(02)00597-3	journal	September 2002
Infrared length scale and extrapolations for the no-core shell model Wendt, K. A.; Forssén, C.; Papenbrock, T. Physical Review C, Vol. 91, Issue 6 https://doi.org/10.1103/PhysRevC.91.061301	journal	June 2015
Approximation by superpositions of a sigmoidal function Cybenko, G. Mathematics of Control, Signals, and Systems, Vol. 2, Issue 4 https://doi.org/10.1007/BF02551274	journal	December 1989
Coulomb-Sturmian basis for the nuclear many-body problem Caprio, M. A.; Maris, P.; Vary, J. P. Physical Review C, Vol. 86, Issue 3 https://doi.org/10.1103/PhysRevC.86.034312	journal	September 2012
Accurate charge-dependent nucleon-nucleon potential at fourth order of chiral perturbation theory Entem, D. R.; Machleidt, R. Physical Review C, Vol. 68, Issue 4 https://doi.org/10.1103/PhysRevC.68.041001	journal	October 2003
Center-of-Mass Motion in Brueckner Theory for a Finite Nucleus Lipkin, Harry J. Physical Review, Vol. 109, Issue 6 https://doi.org/10.1103/PhysRev.109.2071	journal	March 1958
Accurate nucleon–nucleon potential based upon chiral perturbation theory Entem, D. R.; Machleidt, R. Physics Letters B, Vol. 524, Issue 1-2 https://doi.org/10.1016/S0370-2693(01)01363-6	journal	January 2002
Datasets of seed mucilage traits for Arabidopsis thaliana natural accessions with atypical outer mucilage Cambert, Mireille; Berger, Adeline; Sallé, Christine Scientific Data, Vol. 8, Issue 1 https://doi.org/10.1038/s41597-021-00857-3	journal	March 2021
Ab initio nuclear structure – the large sparse matrix eigenvalue problem Vary, James P.; Maris, Pieter; Ng, Esmond Journal of Physics: Conference Series, Vol. 180 https://doi.org/10.1088/1742-6596/180/1/012083	journal	July 2009
Loosely bound three-body nuclear systems in the J-matrix approach Lurie, Yu. A.; Shirokov, A. M. Annals of Physics, Vol. 312, Issue 2 https://doi.org/10.1016/j.aop.2004.02.002	journal	August 2004
Impact parameter determination for heavy-ion collisions by use of a neural network David, Christophe; Freslier, Marc; Aichelin, Jörg Physical Review C, Vol. 51, Issue 3 https://doi.org/10.1103/PhysRevC.51.1453	journal	March 1995
AB INITIO NUCLEAR STRUCTURE CALCULATIONS OF p-SHELL NUCLEI WITH JISP16 Maris, Pieter; Vary, James P. International Journal of Modern Physics E, Vol. 22, Issue 07 https://doi.org/10.1142/S0218301313300166	journal	July 2013
Training feedforward networks with the Marquardt algorithm Hagan, M. T.; Menhaj, M. B. IEEE Transactions on Neural Networks, Vol. 5, Issue 6 https://doi.org/10.1109/72.329697	journal	January 1994
An Algorithm for Least-Squares Estimation of Nonlinear Parameters Marquardt, Donald W. Journal of the Society for Industrial and Applied Mathematics, Vol. 11, Issue 2 https://doi.org/10.1137/0111030	journal	June 1963
Recent experimental progress in nuclear halo structure studies Tanihata, Isao; Savajols, Herve; Kanungo, Rituparna Progress in Particle and Nuclear Physics, Vol. 68 https://doi.org/10.1016/j.ppnp.2012.07.001	journal	January 2013
Refining mass formulas for astrophysical applications: A Bayesian neural network approach Utama, R.; Piekarewicz, J. Physical Review C, Vol. 96, Issue 4 https://doi.org/10.1103/PhysRevC.96.044308	journal	October 2017
Multilayer feedforward networks are universal approximators Hornik, Kurt; Stinchcombe, Maxwell; White, Halbert Neural Networks, Vol. 2, Issue 5 https://doi.org/10.1016/0893-6080(89)90020-8	journal	January 1989
N3LO NN interaction adjusted to light nuclei in ab exitu approach Shirokov, A. M.; Shin, I. J.; Kim, Y. Physics Letters B, Vol. 761 https://doi.org/10.1016/j.physletb.2016.08.006	journal	October 2016
Similarity renormalization group for nucleon-nucleon interactions Bogner, S. K.; Furnstahl, R. J.; Perry, R. J. Physical Review C, Vol. 75, Issue 6 https://doi.org/10.1103/PhysRevC.75.061001	journal	June 2007
Bayesian Interpolation MacKay, David J. C. Neural Computation, Vol. 4, Issue 3 https://doi.org/10.1162/neco.1992.4.3.415	journal	May 1992
The Symmetric Eigenvalue Problem Parlett, Beresford N. Classics in Applied Mathematics https://doi.org/10.1137/1.9781611971163	book	January 1998
Improving the scalability of a symmetric iterative eigensolver for multi-core platforms: IMPROVING THE SCALABILITY OF A SYMMETRIC ITERATIVE EIGENSOLVER Aktulga, Hasan Metin; Yang, Chao; Ng, Esmond G. Concurrency and Computation: Practice and Experience, Vol. 26, Issue 16 https://doi.org/10.1002/cpe.3129	journal	September 2013
Halo nuclei ${}^{6}{He}$ and ${}^{8}{He}$ with the Coulomb-Sturmian basis Caprio, M. A.; Maris, P.; Vary, J. P. Physical Review C, Vol. 90, Issue 3 https://doi.org/10.1103/PhysRevC.90.034305	journal	September 2014
Universal properties of infrared oscillator basis extrapolations More, S. N.; Ekström, A.; Furnstahl, R. J. Physical Review C, Vol. 87, Issue 4 https://doi.org/10.1103/PhysRevC.87.044326	journal	April 2013
Erratum: Coarse-grained potential analysis of neutron-proton and proton-proton scattering below the pion production threshold [Phys. Rev. C 88 , 064002 (2013)] Navarro Pérez, R.; Amaro, J. E.; Arriola, E. Ruiz Physical Review C, Vol. 91, Issue 2 https://doi.org/10.1103/PhysRevC.91.029901	journal	February 2015
Ab initio no-core solutions for ⁶ Li Shin, Ik Jae; Kim, Youngman; Maris, Pieter Journal of Physics G: Nuclear and Particle Physics, Vol. 44, Issue 7 https://doi.org/10.1088/1361-6471/aa6cb7	journal	May 2017
Nuclear charge radii: density functional theory meets Bayesian neural networks Utama, R.; Chen, Wei-Chia; Piekarewicz, J. Journal of Physics G: Nuclear and Particle Physics, Vol. 43, Issue 11 https://doi.org/10.1088/0954-3899/43/11/114002	journal	October 2016
An artificial neural network application on nuclear charge radii Akkoyun, S.; Bayram, T.; Kara, S. O. Journal of Physics G: Nuclear and Particle Physics, Vol. 40, Issue 5 https://doi.org/10.1088/0954-3899/40/5/055106	journal	March 2013
Covariant spectator theory of $np$ scattering: Phase shifts obtained from precision fits to data below 350 MeV Gross, Franz; Stadler, Alfred Physical Review C, Vol. 78, Issue 1 https://doi.org/10.1103/PhysRevC.78.014005	journal	July 2008
Decoding $β$ -decay systematics: A global statistical model for $β^{-}$ half-lives Costiris, N. J.; Mavrommatis, E.; Gernoth, K. A. Physical Review C, Vol. 80, Issue 4 https://doi.org/10.1103/PhysRevC.80.044332	journal	October 2009
Validating neural-network refinements of nuclear mass models Utama, R.; Piekarewicz, J. Physical Review C, Vol. 97, Issue 1 https://doi.org/10.1103/PhysRevC.97.014306	journal	January 2018
Bayesian approach to model-based extrapolation of nuclear observables Neufcourt, Léo; Cao, Yuchen; Nazarewicz, Witold Physical Review C, Vol. 98, Issue 3 https://doi.org/10.1103/PhysRevC.98.034318	journal	September 2018
Convergence properties of ab initio calculations of light nuclei in a harmonic oscillator basis Coon, S. A.; Avetian, M. I.; Kruse, M. K. G. Physical Review C, Vol. 86, Issue 5 https://doi.org/10.1103/PhysRevC.86.054002	journal	November 2012
Corrections to nuclear energies and radii in finite oscillator spaces Furnstahl, R. J.; Hagen, G.; Papenbrock, T. Physical Review C, Vol. 86, Issue 3 https://doi.org/10.1103/PhysRevC.86.031301	journal	September 2012
Corrections to nucleon capture cross sections computed in truncated Hilbert spaces Acharya, B.; Ekström, A.; Odell, D. Physical Review C, Vol. 95, Issue 3 https://doi.org/10.1103/PhysRevC.95.031301	journal	March 2017
Approximation by superpositions of a sigmoidal function Cybenko, G. Mathematics of Control, Signals, and Systems, Vol. 5, Issue 4 https://doi.org/10.1007/bf02134016	journal	December 1992
Ab initio no-core full configuration calculations of light nuclei Maris, P.; Vary, J. P.; Shirokov, A. M. Physical Review C, Vol. 79, Issue 1 https://doi.org/10.1103/PhysRevC.79.014308	journal	January 2009
Nuclear mass systematics using neural networks Athanassopoulos, S.; Mavrommatis, E.; Gernoth, K. A. Nuclear Physics A, Vol. 743, Issue 4 https://doi.org/10.1016/j.nuclphysa.2004.08.006	journal	November 2004
Natural orbital description of the halo nucleus 6He Constantinou, Chrysovalantis; Caprio, Mark A.; Vary, James P. Nuclear Science and Techniques, Vol. 28, Issue 12 https://doi.org/10.1007/s41365-017-0332-6	journal	November 2017
Impact parameter determination in experimental analysis using a neural network Haddad, F.; Hagel, K.; Li, J. Physical Review C, Vol. 55, Issue 3 https://doi.org/10.1103/PhysRevC.55.1371	journal	March 1997
Infrared extrapolations of quadrupole moments and transitions Odell, D.; Papenbrock, T.; Platter, L. Physical Review C, Vol. 93, Issue 4 https://doi.org/10.1103/PhysRevC.93.044331	journal	April 2016
From low-momentum interactions to nuclear structure Bogner, S. K.; Furnstahl, R. J.; Schwenk, A. Progress in Particle and Nuclear Physics, Vol. 65, Issue 1 https://doi.org/10.1016/j.ppnp.2010.03.001	journal	July 2010
Accurate nucleon-nucleon potential based upon chiral perturbation theory Entem, D. R.; Machleidt, R. NUCLEAR PHYSICS IN THE 21st CENTURY:International Nuclear Physics Conference INPC 2001, AIP Conference Proceedings https://doi.org/10.1063/1.1469952	conference	January 2002
Covariant spectator theory of np scattering: Phase shifts obtained from precision fits to data below 350 MeV Gross, Franz; Stadler, Alfred arXiv https://doi.org/10.48550/arxiv.0802.1552	text	January 2008
Ab initio no-core full configuration calculations of light nuclei Maris, P.; Vary, J. P.; Shirokov, A. M. arXiv https://doi.org/10.48550/arxiv.0808.3420	text	January 2008
{\it Ab initio} nuclear structure - the large sparse matrix eigenvalue problem Vary, James P.; Maris, Pieter; Ng, Esmond arXiv https://doi.org/10.48550/arxiv.0907.0209	text	January 2009
From low-momentum interactions to nuclear structure Bogner, S. K.; Furnstahl, R. J.; Schwenk, A. arXiv https://doi.org/10.48550/arxiv.0912.3688	text	January 2009
Corrections to nuclear energies and radii in finite oscillator spaces Furnstahl, R. J.; Hagen, G.; Papenbrock, T. arXiv https://doi.org/10.48550/arxiv.1207.6100	text	January 2012
Infrared length scale and extrapolations for the no-core shell model Wendt, K. A.; Forssén, C.; Papenbrock, T. arXiv https://doi.org/10.48550/arxiv.1503.07144	text	January 2015
Natural orbital description of the halo nucleus 6He Constantinou, Ch.; Caprio, M. A.; Vary, J. P. arXiv https://doi.org/10.48550/arxiv.1605.04976	text	January 2016
Nuclear charge radii: Density functional theory meets Bayesian neural networks Utama, Raditya; Chen, Wei-Chia; Piekarewicz, Jorge arXiv https://doi.org/10.48550/arxiv.1608.03020	text	January 2016
Corrections to nucleon capture cross sections computed in truncated Hilbert spaces Acharya, B.; Ekström, A.; Odell, D. arXiv https://doi.org/10.48550/arxiv.1608.04699	text	January 2016
Refining mass formulas for astrophysical applications: a Bayesian neural network approach Utama, Raditya; Piekarewicz, Jorge arXiv https://doi.org/10.48550/arxiv.1704.06632	text	January 2017
Validating neural-network refinements of nuclear mass models Utama, R.; Piekarewicz, J. arXiv https://doi.org/10.48550/arxiv.1709.09502	text	January 2017
Large-scale exact diagonalizations reveal low-momentum scales of nuclei Forssén, C.; Carlsson, B. D.; Johansson, H. T. arXiv https://doi.org/10.48550/arxiv.1712.09951	text	January 2017
Bayesian approach to model-based extrapolation of nuclear observables Neufcourt, Léo; Cao, Yuchen; Nazarewicz, Witold arXiv https://doi.org/10.48550/arxiv.1806.00552	text	January 2018
Accurate Nucleon-Nucleon Potential Based upon Chiral Perturbation Theory Entem, D. R.; Machleidt, R. arXiv https://doi.org/10.48550/arxiv.nucl-th/0108057	text	January 2001
Accurate Charge-Dependent Nucleon-Nucleon Potential at Fourth Order of Chiral Perturbation Theory Entem, D. R.; Machleidt, R. arXiv https://doi.org/10.48550/arxiv.nucl-th/0304018	text	January 2003
Loosely bound three-body nuclear systems in the J-matrix approach Lurie, Yu. A.; Shirokov, A. M. arXiv https://doi.org/10.48550/arxiv.nucl-th/0312028	text	January 2003
Nucleon-nucleon interaction in the $J$-matrix inverse scattering approach and few-nucleon systems Shirokov, A. M.; Mazur, A. I.; Zaytsev, S. A. arXiv https://doi.org/10.48550/arxiv.nucl-th/0312029	text	January 2003

Similar Records

Deep learning: Extrapolation tool for ab initio nuclear theory

Journal Article · Wed May 01 00:00:00 EDT 2019 · Physical Review C · OSTI ID:1603455

Negoita, Gianina Alina; Vary, James P.; Luecke, Glenn R.; +8 more

Ground-state properties of light 4n self-conjugate nuclei in ab initio no-core Monte Carlo shell model calculations with nonlocal N N interactions

Journal Article · Wed Nov 24 00:00:00 EST 2021 · Physical Review. C · OSTI ID:1603455

Abe, T.; Maris, P.; Otsuka, T.; +3 more

Ab initio no-core solutions for ⁶Li

Journal Article · Wed May 31 00:00:00 EDT 2017 · Journal of Physics. G, Nuclear and Particle Physics · OSTI ID:1603455

Shin, Ik Jae; Kim, Youngman; Maris, Pieter; +4 more

Related Subjects

73 NUCLEAR PHYSICS AND RADIATION PHYSICS
Artificial Neural Networks
No-Core Shell Model
6Li
ground state energy
root mean square radius
extrapolation

Title: Deep learning: Extrapolation tool for ab initio nuclear theory

Citation Formats

References (68)

Similar Records

Related Subjects