Amortized Simulation-Based Inference of Relativistic Mean-Field Couplings for Neutron-Star Equations of State

Abstract: We present a simulation-based inference framework for constraining microscopic relativistic mean-field parameters of neutron-star equations of state. Neural posterior estimation is applied to two representative RMF families, a density-dependent DDB model and a nonlinear RMF-NL model, using nuclear saturation properties, chiral effective-field-theory pure-neutron-matter pressures, and the maximum-mass constraint as conditioning observables. The inferred posteriors are validated against the conventional nested sampler (PyMultiNest) calculations and tested with the TARP coverage diagnostic. For both RMF parametrizations, the neural posterior reproduces the nested-sampling constraints on model couplings, nuclear-matter properties, and neutron-star observables with no significant bias. The amortized estimator generates $3\times 10^{4}$ posterior samples in about $2.5\,\mathrm{s}$ on a CPU, enabling a rapid inference workflow without the need for retraining for updated data. This constitutes a proof of concept that NPE-emulated RMF models, once validated, can be safely used for superfast exploratory inference. As an additional mock-observation test, imposing $R_{1.4}=12\,{\rm km}$ and $M_{\rm max}>1.97\,M_\odot$ leads to consistent predictions for the maximum-mass configuration, with DDB giving $M_{\rm max}=2.10^{+0.09}{-0.07}\,M\odot$, $R_{\rm max}=10.71^{+0.14}_{-0.21}\,{\rm km}$ and RMF-NL giving $M_{\rm max}=2.05^{+0.10}{-0.06}\,M\odot$, $R_{\rm max}=10.69^{+0.18}_{-0.19}\,{\rm km}$; although fixing $R_{1.4}$ confines both families to a narrow EOS region, RMF-NL remains marginally softer than DDB at high density, consistent with its slightly lower maximum mass.