Generative Modeling of Nucleon-Nucleon Interactions

Developing high-precision models of the nuclear force and propagating the associated uncertainties in quantum many-body calculations of nuclei and nuclear matter remain key challenges for ab initio nuclear theory. In this Letter, we demonstrate that generative machine learning models can construct novel instances of the nucleon-nucleon interaction when trained on existing potentials from the literature. In particular, we train the generative model on nucleon-nucleon potentials derived at second and third order in chiral effective field theory and at three different choices of the resolution scale. We then show that the model can be used to generate samples of the nucleon-nucleon potential drawn from a continuous distribution in the resolution scale parameter space. The generated potentials are shown to produce high-quality nucleon-nucleon scattering phase shifts. This work provides an important step toward a comprehensive estimation of theoretical uncertainties in nuclear many-body calculations that arise from the arbitrary choice of nuclear interaction and resolution scale.