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

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 ab initio nuclear structure. We show that FeynmanNet can provide very accurate solutions of ground-state energies and wave functions for 4He, 6Li, and even up to 16O 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 ab initio method for predicting nuclear properties based on the realistic interactions between nucleons.

Automated summary

By combining the essential physics of nuclear wave functions and the strong expressive power of artificial neural networks, FeynmanNet has been developed as a deep-learning variational quantum Monte Carlo approach for predicting nuclear structure from first principles. It achieves very accurate solutions for ground-state energies and wave functions of helium-4, lithium-6, and oxygen-16, even considering the complex interactions between nucleons. Compared to conventional diffusion Monte Carlo approaches, FeynmanNet overcomes the fermion-sign problem and scales polynomially with nucleon numbers, making it a highly accurate and efficient method for ab initio nuclear structure prediction.