Neural-Network Extraction of Nucleon-Nucleon Contact Constants from Phase Shifts

Abstract This work is a neural-network based approach to the inverse scattering of the Nucleon-Nucleon Potential. We infer short-range contact low-energy constants for a truncated model space from phase shifts. A simplified interaction model combining one-pion exchange (OPE) and contact interactions is used to generate synthetic scattering data. The forward scattering problem is solved numerically using a discretized Lippmann–Schwinger equation. A multilayer percep- tron is trained to map phase-shift data to eight contact LECs. The network uses 66 input features obtained from six uncoupled partial-wave channels evaluated at eleven energies. A synthetic dataset containing 5,000 parame- ter samples is generated. The trained network provides initial parameter estimates, which are subsequently refined through bounded least-squares optimization against Nijmegen PWA phase shifts. The results illustrate the potential of combining neural networks with physics-based optimization. Since the forward model is approximate and omits contributions present in more complete nuclear interactions, the inferred LECs need not coincide with published parameter values. The performance of the method is therefore assessed primarily through parameter recovery and reconstruction of the scattering data. The fitted constants are interpreted as effective parameters within the chosen truncated interaction model and are not taken to demonstrate renormalization or physical equivalence with constants from more complete interactions.