Variational Monte Carlo Calculations of A ≤ 4 Nuclei with an Artificial Neural-Network Correlator Ansatz

Adams, Corey; Carleo, Giuseppe; Lovato, Alessandro; Rocco, Noemi

doi:10.1103/physrevlett.127.022502

Variational Monte Carlo Calculations of A ≤ 4 Nuclei with an Artificial Neural-Network Correlator Ansatz

Journal Article · Wed Jul 07 00:00:00 EDT 2021 · Physical Review Letters

DOI:https://doi.org/10.1103/physrevlett.127.022502· OSTI ID:1864334

Adams, Corey ^[1]; Carleo, Giuseppe ^[2]; ^[3]; Rocco, Noemi ^[4]

Argonne National Lab. (ANL), Argonne, IL (United States)
Ecole Polytechnique Federale Lausanne (Switzerland)
Argonne National Lab. (ANL), Argonne, IL (United States); Istituto Nazionale di Fisica Nucleare, Trento (Italy)
Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)

Here, the complexity of many-body quantum wave functions is a central aspect of several fields of physics and chemistry where nonperturbative interactions are prominent. Artificial neural networks (ANNs) have proven to be a flexible tool to approximate quantum many-body states in condensed matter and chemistry problems. In this work we introduce a neural-network quantum state ansatz to model the ground-state wave function of light nuclei, and approximately solve the nuclear many-body Schrodinger equation. Using efficient stochastic sampling and optimization schemes, our approach extends pioneering applications of ANNs in the field, which present exponentially scaling algorithmic complexity. We compute the binding energies and point-nucleon densities of A ≤ 4 nuclei as emerging from a leading-order pionless effective field theory Hamiltonian. We successfully benchmark the ANN wave function against more conventional parametrizations based on two- and three-body Jastrow functions, and virtually exact Green's function Monte Carlo results.

View Accepted Manuscript (DOE)

Research Organization:: Argonne National Laboratory (ANL), Argonne, IL (United States); Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States)

Sponsoring Organization:: Fermi Research Alliance; NUCLEI SciDAC Program; USDOE Office of Science (SC), High Energy Physics (HEP); USDOE Office of Science (SC), Nuclear Physics (NP)

Grant/Contract Number:: AC02-06CH11357; AC02-07CH11359

OSTI ID:: 1864334

Alternate ID(s):: OSTI ID: 1659453

Journal Information:: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 2 Vol. 127; ISSN 0031-9007

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (50)

Monte Carlo calculations of triton and 4He nuclei with the Reid potential Lomnitz-Adler, J.; Pandharipande, V. R.; Smith, R. A. Nuclear Physics A, Vol. 361, Issue 2 https://doi.org/10.1016/0375-9474(81)90642-4	journal	May 1981
A quantum Monte Carlo method for nucleon systems Schmidt, K. E.; Fantoni, S. Physics Letters B, Vol. 446, Issue 2 https://doi.org/10.1016/S0370-2693(98)01522-6	journal	January 1999
On the momentum term in gradient descent learning algorithms Qian, Ning Neural Networks, Vol. 12, Issue 1 https://doi.org/10.1016/S0893-6080(98)00116-6	journal	January 1999
Ground-state properties of 4 He and 16 O extrapolated from lattice QCD with pionless EFT Contessi, L.; Lovato, A.; Pederiva, F. Physics Letters B, Vol. 772 https://doi.org/10.1016/j.physletb.2017.07.048	journal	September 2017
Short-range correlations and the charge density Weiss, Ronen; Schmidt, Axel; Miller, Gerald A. Physics Letters B, Vol. 790 https://doi.org/10.1016/j.physletb.2019.01.053	journal	March 2019
Machine learning the deuteron Keeble, J. W. T.; Rios, A. Physics Letters B, Vol. 809 https://doi.org/10.1016/j.physletb.2020.135743	journal	October 2020
Chiral effective field theory and nuclear forces Machleidt, R.; Entem, D. R. Physics Reports, Vol. 503, Issue 1 https://doi.org/10.1016/j.physrep.2011.02.001	journal	June 2011
The In-Medium Similarity Renormalization Group: A novel ab initio method for nuclei Hergert, H.; Bogner, S. K.; Morris, T. D. Physics Reports, Vol. 621 https://doi.org/10.1016/j.physrep.2015.12.007	journal	March 2016
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
Fermionic neural-network states for ab-initio electronic structure Choo, Kenny; Mezzacapo, Antonio; Carleo, Giuseppe Nature Communications, Vol. 11, Issue 1 https://doi.org/10.1038/s41467-020-15724-9	journal	May 2020
Deep-neural-network solution of the electronic Schrödinger equation Hermann, Jan; Schätzle, Zeno; Noé, Frank Nature Chemistry, Vol. 12, Issue 10 https://doi.org/10.1038/s41557-020-0544-y	journal	September 2020
Equation of State Calculations by Fast Computing Machines Metropolis, Nicholas; Rosenbluth, Arianna W.; Rosenbluth, Marshall N. The Journal of Chemical Physics, Vol. 21, Issue 6 https://doi.org/10.1063/1.1699114	journal	June 1953
Optimization of quantum Monte Carlo wave functions by energy minimization Toulouse, Julien; Umrigar, C. J. The Journal of Chemical Physics, Vol. 126, Issue 8 https://doi.org/10.1063/1.2437215	journal	February 2007
SchNet – A deep learning architecture for molecules and materials Schütt, K. T.; Sauceda, H. E.; Kindermans, P. -J. The Journal of Chemical Physics, Vol. 148, Issue 24 https://doi.org/10.1063/1.5019779	journal	June 2018
Coupled-cluster computations of atomic nuclei Hagen, G.; Papenbrock, T.; Hjorth-Jensen, M. Reports on Progress in Physics, Vol. 77, Issue 9 https://doi.org/10.1088/0034-4885/77/9/096302	journal	September 2014
Exact restoration of Galilei invariance in density functional calculations with quantum Monte Carlo Massella, P.; Barranco, F.; Lonardoni, D. Journal of Physics G: Nuclear and Particle Physics, Vol. 47, Issue 3 https://doi.org/10.1088/1361-6471/ab588c	journal	January 2020
Monte Carlo sampling methods using Markov chains and their applications Hastings, W. K. Biometrika, Vol. 57, Issue 1 https://doi.org/10.1093/biomet/57.1.97	journal	April 1970
Neural Gutzwiller-projected variational wave functions Ferrari, Francesco; Becca, Federico; Carrasquilla, Juan Physical Review B, Vol. 100, Issue 12 https://doi.org/10.1103/PhysRevB.100.125131	journal	September 2019
Wave function optimization in the variational Monte Carlo method Sorella, Sandro Physical Review B, Vol. 71, Issue 24 https://doi.org/10.1103/PhysRevB.71.241103	journal	June 2005
Restricted Boltzmann machine learning for solving strongly correlated quantum systems Nomura, Yusuke; Darmawan, Andrew S.; Yamaji, Youhei Physical Review B, Vol. 96, Issue 20 https://doi.org/10.1103/PhysRevB.96.205152	journal	November 2017
Constructing neural stationary states for open quantum many-body systems Yoshioka, Nobuyuki; Hamazaki, Ryusuke Physical Review B, Vol. 99, Issue 21 https://doi.org/10.1103/PhysRevB.99.214306	journal	June 2019
Extrapolation of nuclear structure observables with artificial neural networks Jiang, W. G.; Hagen, G.; Papenbrock, T. Physical Review C, Vol. 100, Issue 5 https://doi.org/10.1103/PhysRevC.100.054326	journal	November 2019
Benchmark calculations of pure neutron matter with realistic nucleon-nucleon interactions Piarulli, M.; Bombaci, I.; Logoteta, D. Physical Review C, Vol. 101, Issue 4 https://doi.org/10.1103/PhysRevC.101.045801	journal	April 2020
Two- and three-nucleon contact interactions and ground-state energies of light- and medium-mass nuclei Schiavilla, R.; Girlanda, L.; Gnech, A. Physical Review C, Vol. 103, Issue 5 https://doi.org/10.1103/PhysRevC.103.054003	journal	May 2021
Self-consistent Green's functions formalism with three-body interactions Carbone, Arianna; Cipollone, Andrea; Barbieri, Carlo Physical Review C, Vol. 88, Issue 5 https://doi.org/10.1103/PhysRevC.88.054326	journal	November 2013
Spectra and scattering of light lattice nuclei from effective field theory Kirscher, J.; Barnea, N.; Gazit, D. Physical Review C, Vol. 92, Issue 5 https://doi.org/10.1103/PhysRevC.92.054002	journal	November 2015
Deep learning: Extrapolation tool for ab initio nuclear theory Negoita, Gianina Alina; Vary, James P.; Luecke, Glenn R. Physical Review C, Vol. 99, Issue 5 https://doi.org/10.1103/PhysRevC.99.054308	journal	May 2019
Ab Initio Calculation of the Hoyle State Epelbaum, Evgeny; Krebs, Hermann; Lee, Dean Physical Review Letters, Vol. 106, Issue 19 https://doi.org/10.1103/PhysRevLett.106.192501	journal	May 2011
Charge Form Factor and Sum Rules of Electromagnetic Response Functions in C 12 Lovato, A.; Gandolfi, S.; Butler, Ralph Physical Review Letters, Vol. 111, Issue 9 https://doi.org/10.1103/PhysRevLett.111.092501	journal	August 2013
Effective Field Theory for Lattice Nuclei Barnea, N.; Contessi, L.; Gazit, D. Physical Review Letters, Vol. 114, Issue 5 https://doi.org/10.1103/PhysRevLett.114.052501	journal	February 2015
Symmetries and Many-Body Excitations with Neural-Network Quantum States Choo, Kenny; Carleo, Giuseppe; Regnault, Nicolas Physical Review Letters, Vol. 121, Issue 16 https://doi.org/10.1103/PhysRevLett.121.167204	journal	October 2018
Variational Quantum Monte Carlo Method with a Neural-Network Ansatz for Open Quantum Systems Nagy, Alexandra; Savona, Vincenzo Physical Review Letters, Vol. 122, Issue 25 https://doi.org/10.1103/PhysRevLett.122.250501	journal	June 2019
Neural-Network Approach to Dissipative Quantum Many-Body Dynamics Hartmann, Michael J.; Carleo, Giuseppe Physical Review Letters, Vol. 122, Issue 25 https://doi.org/10.1103/PhysRevLett.122.250502	journal	June 2019
Variational Neural-Network Ansatz for Steady States in Open Quantum Systems Vicentini, Filippo; Biella, Alberto; Regnault, Nicolas Physical Review Letters, Vol. 122, Issue 25 https://doi.org/10.1103/PhysRevLett.122.250503	journal	June 2019
Green Function Monte Carlo with Stochastic Reconfiguration Sorella, Sandro Physical Review Letters, Vol. 80, Issue 20 https://doi.org/10.1103/PhysRevLett.80.4558	journal	May 1998
Renormalization of the Three-Body System with Short-Range Interactions Bedaque, P. F.; Hammer, H. -W.; van Kolck, U. Physical Review Letters, Vol. 82, Issue 3 https://doi.org/10.1103/PhysRevLett.82.463	journal	January 1999
Nuclear and neutron-star matter from local chiral interactions Lonardoni, D.; Tews, I.; Gandolfi, S. Physical Review Research, Vol. 2, Issue 2 https://doi.org/10.1103/PhysRevResearch.2.022033	journal	May 2020
Ab initio solution of the many-electron Schrödinger equation with deep neural networks Pfau, David; Spencer, James S.; Matthews, Alexander G. D. G. Physical Review Research, Vol. 2, Issue 3 https://doi.org/10.1103/PhysRevResearch.2.033429	journal	September 2020
Modern theory of nuclear forces Epelbaum, E.; Hammer, H. -W.; Meißner, Ulf-G. Reviews of Modern Physics, Vol. 81, Issue 4 https://doi.org/10.1103/RevModPhys.81.1773	journal	December 2009
Quantum Monte Carlo methods for nuclear physics Carlson, J.; Gandolfi, S.; Pederiva, F. Reviews of Modern Physics, Vol. 87, Issue 3 https://doi.org/10.1103/RevModPhys.87.1067	journal	September 2015
Machine learning and the physical sciences Carleo, Giuseppe; Cirac, Ignacio; Cranmer, Kyle Reviews of Modern Physics, Vol. 91, Issue 4 https://doi.org/10.1103/RevModPhys.91.045002	journal	December 2019
Nuclear effective field theory: Status and perspectives Hammer, H. -W.; König, Sebastian; van Kolck, U. Reviews of Modern Physics, Vol. 92, Issue 2 https://doi.org/10.1103/RevModPhys.92.025004	journal	June 2020
Solving the quantum many-body problem with artificial neural networks Carleo, Giuseppe; Troyer, Matthias Science, Vol. 355, Issue 6325 https://doi.org/10.1126/science.aag2302	journal	February 2017
Do we know how to count powers in pionless and pionful effective field theory? Yang, C. -J. The European Physical Journal A, Vol. 56, Issue 3 https://doi.org/10.1140/epja/s10050-020-00104-0	journal	March 2020
E FFECTIVE F IELD T HEORY FOR F EW -N UCLEON S YSTEMS Bedaque, Paulo F.; van Kolck, Ubirajara Annual Review of Nuclear and Particle Science, Vol. 52, Issue 1 https://doi.org/10.1146/annurev.nucl.52.050102.090637	journal	December 2002
Natural Gradient Works Efficiently in Learning Amari, Shun-ichi Neural Computation, Vol. 10, Issue 2 https://doi.org/10.1162/089976698300017746	journal	February 1998
Atomic Nuclei From Quantum Monte Carlo Calculations With Chiral EFT Interactions Gandolfi, Stefano; Lonardoni, Diego; Lovato, Alessandro Frontiers in Physics, Vol. 8 https://doi.org/10.3389/fphy.2020.00117	journal	April 2020
Perspectives on Nuclear Structure and Scattering with the Ab Initio No-Core Shell Model Vary, James P.; Maris, Pieter; Fasano, Patrick J. Proceedings of the Ito International Research Center Symposium "Perspectives of the Physics of Nuclear Structure" https://doi.org/10.7566/JPSCP.23.012001	conference	December 2018
Method to Solve Quantum Few-Body Problems with Artificial Neural Networks Saito, Hiroki Journal of the Physical Society of Japan, Vol. 87, Issue 7 https://doi.org/10.7566/JPSJ.87.074002	journal	July 2018
Machine Learning Quantum States — Extensions to Fermion–Boson Coupled Systems and Excited-State Calculations Nomura, Yusuke Journal of the Physical Society of Japan, Vol. 89, Issue 5 https://doi.org/10.7566/JPSJ.89.054706	journal	May 2020

Similar Records

Variational Monte Carlo Calculations of A≤4 Nuclei with an Artificial Neural-Network Correlator Ansatz

Journal Article · Tue Jul 06 20:00:00 EDT 2021 · Phys.Rev.Lett. · OSTI ID:1659453

Variational Neural-Network Ansatz for Continuum Quantum Field Theory

Journal Article · Wed Aug 23 20:00:00 EDT 2023 · Physical Review Letters · OSTI ID:2425552

Related Subjects

73 NUCLEAR PHYSICS AND RADIATION PHYSICS
nuclear decays
nuclear many-body theory
nuclear structure
nucleon distribution

Variational Monte Carlo Calculations of A ≤ 4 Nuclei with an Artificial Neural-Network Correlator Ansatz

Citation Formats

References (50)

Similar Records

Related Subjects