Efficient emulation of nuclear ground states with neural-network variational Monte Carlo and eigenvector continuation

Abstract

An efficient emulator for \emph{ab initio} calculations of nuclear ground-state properties is developed by integrating the neural-network variational Monte Carlo framework, FeynmanNet, with the eigenvector continuation. It enables the calculation of observables for different Hamiltonians with minimal computational cost, while delivering ground-state energies with errors below $0.5\%$ compared to the full FeynmanNet results. With this emulator, the ground-state energies and charge radii of ${}^{16}\mathrm{O}$, ${}^{15}\mathrm{O}$, ${}^{14}\mathrm{O}$, ${}^{15}\mathrm{N}$, and ${}^{14}\mathrm{C}$ are computed using a nuclear Hamiltonian derived from the leading-order pionless effective field theory, with a large number of different values of low-energy constants (LECs). Then, we perform a global sensitivity analysis of the ground-state energies, charge radii, separation energies of selected nuclei for the three LECs in the Hamiltonian, to identify how each LEC contributes to the variances of these observables. It shows that the two-body LEC in the ${}^3{S}_1$ channel is the most influential LEC governing these nuclear bulk properties. Finally, the correlations among the ground-state energies of ${}^4$He, ${}^{12}$C, and ${}^{16}$O are investigated by varying the LECs in the Hamiltonian. The analysis reveals that the experimental ground-state energies of ${}^{12}$C and ${}^{16}$O cannot be reproduced simultaneously by varying the LECs in the leading-order pionless Hamiltonian. This suggests that additional ingredients in the leading-order Hamiltonian are required to improve its description of light nuclei. The present work establishes an efficient framework for global sensitivity analysis and uncertainty quantification in the quantum Monte Carlo calculations for light and medium-mass nuclei.

11 pages, 6 figures; published in Physical Review C

References in corpus (57)

• An accurate nucleon-nucleon potential with charge-independence breaking
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• The high-precision, charge-dependent Bonn nucleon-nucleon potential (CD-Bonn)
• Quantum Monte Carlo calculations of nuclei with A \leq 7
• Realistic models of pion-exchange three-nucleon interactions
• Nuclear effective field theory: status and perspectives
• High-quality two-nucleon potentials up to fifth order of the chiral expansion
• Semilocal momentum-space regularized chiral two-nucleon potentials up to fifth order
• Chiral Three-Nucleon Interactions in Light Nuclei, Neutron-$\alpha$ Scattering, and Neutron Matter
• Wave function optimization in the variational Monte Carlo method
• Local chiral effective field theory interactions and quantum Monte Carlo applications
• Nuclear Sizes and the Isotope Shift
• Local chiral potentials and the structure of light nuclei
• Light-nuclei spectra from chiral dynamics
• Eigenvector continuation with subspace learning
• Global sensitivity analysis of bulk properties of an atomic nucleus
• A recipe for EFT uncertainty quantification in nuclear physics
• Nuclear binding near a quantum phase transition
• Eigenvector Continuation as an Efficient and Accurate Emulator for Uncertainty Quantification
• Properties of nuclei up to $A=16$ using local chiral interactions
• Nuclear Physics Around the Unitarity Limit
• Essential elements for nuclear binding
• Variational Monte Carlo calculations of $\mathbf{A}\le 4$ nuclei with an artificial neural-network correlator ansatz
• Scale and Scheme Independence and Position-Momentum Equivalence of Nuclear Short-Range Correlations
• Rigorous constraints on three-nucleon forces in chiral effective field theory from fast and accurate calculations of few-body observables
• Chiral Effective Field Theory Calculations of Weak Transitions in Light Nuclei
• Efficient emulators for scattering using eigenvector continuation
• Improved many-body expansions from eigenvector continuation
• Short Range Correlations and the EMC Effect in Effective Field Theory
• Wavefunction matching for solving quantum many-body problems
• Correlations imposed by the unitary limit between few-nucleon systems, nuclear matter and neutron stars
• Model reduction methods for nuclear emulators
• Fast & accurate emulation of two-body scattering observables without wave functions
• Eigenvector Continuation and Projection-Based Emulators
• Convergence of Eigenvector Continuation
• Perturbative quantum Monte Carlo method for nuclear physics
• Generalizing the calculable $R$-matrix theory and eigenvector continuation to the incoming wave boundary condition
• Two- and three-nucleon contact interactions and ground-state energies of light- and medium-mass nuclei
• Nuclei with up to $\mathbf{A}=6$ nucleons with artificial neural network wave functions
• Deep-neural-network approach to solving the ab initio nuclear structure problem
• Hidden spin-isospin exchange symmetry
• Multiscale physics of atomic nuclei from first principles
• Relativistic effects and three-body interactions in atomic nuclei
• Fast & rigorous predictions for $A=6$ nuclei with Bayesian posterior sampling
• Eigenvector continuation for emulating and extrapolating two-body resonances
• Excited states from eigenvector continuation: the anharmonic oscillator
• Constructing approximate shell-model wavefunctions by eigenvector continuation
• Emulating \emph{ab initio} computations of infinite nucleonic matter
• Wigner SU(4) symmetry, clustering, and the spectrum of ${}^{12}$C
• Volume extrapolation via eigenvector continuation
• Quantum Monte Carlo calculations of magnetic form factors in light nuclei
• A Complex Scaling Method for Efficient and Accurate Scattering Emulation in Nuclear Reactions
• Reconciling light nuclei and nuclear matter: relativistic $abinitio$ calculations
• Towards scalable bound-to-resonance extrapolations for few- and many-body systems
• Sign-Problem-Free Nuclear Quantum Monte Carlo Simulation
• Chiral symmetry and peripheral neutron-$\alpha$ scattering
• Global Framework for Emulation of Nuclear Calculations