Deep-neural-network approach to solving the ab initio nuclear structure problem

Abstract

Predicting the structure of quantum many-body systems from the first principles of quantum mechanics is a common challenge in physics, chemistry, and material science. Deep machine learning has proven to be a powerful tool for solving condensed matter and chemistry problems, while for atomic nuclei it is still quite challenging because of the complicated nucleon-nucleon interactions, which strongly couple the spatial, spin, and isospin degrees of freedom. By combining essential physics of the nuclear wave functions and the strong expressive power of artificial neural networks, we develop FeynmanNet, a deep-learning variational quantum Monte Carlo approach for \emph{ab initio} nuclear structure. We show that FeynmanNet can provide very accurate solutions of ground-state energies and wave functions for ${}^4$He, ${}^6$Li, and even up to ${}^{16}$O as emerging from the leading-order and next-to-leading-order Hamiltonians of pionless effective field theory. Compared to the conventional diffusion Monte Carlo approaches, which suffer from the severe inherent fermion-sign problem, FeynmanNet reaches such a high accuracy in a variational way and scales polynomially with the number of nucleons. Therefore, it paves the way to a highly accurate and efficient \emph{ab initio} method for predicting nuclear properties based on the realistic interactions between nucleons.

16 pages, 4 figures

References in corpus (7)

• Chiral effective field theory and nuclear forces
• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Ab initio predictions link the neutron skin of ${}^{208}$Pb to nuclear forces
• Machine Learning in Nuclear Physics
• Calculation of the ${}^6$Li ground state within the hyperspherical harmonic basis
• Auxiliary Field Diffusion Monte Carlo calculation of nuclei with A<40 with tensor interactions
• Relativistic effects and three-body interactions in atomic nuclei

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• A deep neural network approach to solve the Dirac equation
• Chiral symmetry and peripheral neutron-$\alpha$ scattering
• DeepQuark: A Deep-Neural-Network Approach to Multiquark Bound States
• Neural network expansion of Euclidean path integrals and its application to interacting scalar fields
• Neural Quantum States for Light Nuclei with Chiral Two- and Three-Body Interactions
• Machine learning the single-$\Lambda$ hypernuclei with neural-network quantum states
• Bound on entanglement in neural quantum states
• Efficient emulation of nuclear ground states with neural-network variational Monte Carlo and eigenvector continuation