Neural-Accelerated Bayesian Calibration of Chiral Mean-Field Models to Nuclear Saturation and Vacuum Properties

Chiral models of nuclear interactions provide approximate, phenomenological descriptions of dense matter that respect the symmetries of quantum chromodynamics. Their Lagrangian parameters, however, are difficult to calibrate because these models are not controlled effective theories. Furthermore, repeated model evaluations are computationally expensive, and most parameter choices fail to reproduce acceptable saturation properties or hadron masses in vacuum. To address this, we develop a Bayesian inference framework to identify parameter regions consistent with nuclear saturation properties and vacuum experimental constraints. We implement this framework through a neural-network surrogate approximation that accelerates the repeated mapping from model parameters to nuclear and particle observables. Our fully-modular, neural-accelerated Bayesian framework interfaces the open-source MUSES Calculation Engine, the Bilby inference library, and the PyTorch machine-learning toolkit. We then apply the framework to the chiral mean-field model with a new generalized quartic vector self-interaction sector. We find that viable solutions are rare but broadly distributed within certain regions of parameter space, with the data constraining combinations of couplings more strongly than individual Lagrangian parameters. The resulting degeneracies imply that distinct saturation-compatible models can lead to qualitatively different descriptions of dense nuclear matter and, thus, of neutron stars, highlighting the need to combine terrestrial and astrophysical information.