Building Hadron Potentials from Lattice QCD with Deep Neural Networks

In this study, we develop a deep learning method to learn hadronic interactions unsupervisedly from the correlation functions calculated in lattice QCD simulations. We present our approach of using deep neural networks to model the inter-hadron potentials that are learned from Nambu-Bethe-Salpeter (NBS) wave functions. This enables the incorporation of most general forms of potentials into the Schr\"odinger-type equation for detailed analysis of hadronic interactions. Our results include validations with separable potentials, as well as the local and non-local potentials for the $\Omega_{ccc}-\Omega_{ccc}$ system. The neural networks accurately capture the essential features of these interactions, providing a reliable tool for predicting and analyzing hadron scattering properties, potentially bridging the experimental observables and lattice QCD data.