Normalizing Flows for Generative Modeling of the Nucleon-Nucleon Interaction

Over the past decade, chiral effective field theory has been extensively used to derive models of nuclear many-body forces. Choice of resolution scale and the associated high-momentum regulating function in chiral nuclear interactions are in principle arbitrary and represent a source of uncertainty in the calculation of nuclear many-body observables. Systematically accounting for uncertainties due to the regulating function is challenging, so in the present work we explore the use of generative modeling to propose new regulated interactions based on a set of training samples. Using normalizing-flow models (NFs) from machine learning, we seek to create a model that can learn a distribution of matrix elements for any appropriate cutoff value, from which we can sample new potentials at different cutoffs. We attempt two NF architectures, the Glow model [1] and a similar model without multi-scale architecture, which we call cFlow. As a test case, the models are trained on a set of low-momentum and similarity renormalization group evolved potentials. We show the effectiveness of the NF models by reconstructing the initial potentials and generating new matrix elements for validation samples. Future work will involve testing the models on a set of high-precision chiral nuclear forces.