Neural Network Construction of the Equation of State from Relativistic ab initio Calculations
Constraining the nuclear matter equation of state (EOS) beyond saturation density is a central goal of nuclear physics and astrophysics. While the relativistic Brueckner-Hartree-Fock (RBHF) theory, an \textit{ab initio,} non-perturbative nuclear many-body theory starting from realistic interactions, accurately describes nuclear matter properties near the saturation density $\rho_0 \approx 0.16$ fm$^{-3}$, its applicability is currently limited to densities up to $3 \rho_0$, necessitating a reliable extrapolation to higher densities. In this work, we employ supervised machine learning to train thousands of fully connected neural networks on low-density RBHF data. By enforcing thermodynamic consistency and smoothness, we finally select a subset of 264 optimal models. These models employ the Swish activation function, which we identify as the most reliable choice for stable extrapolation after extensive testing and comparison. Using these models to extend the EOS over the full density range, we obtain the nuclear matter symmetry energy and then compute the neutron star mass-radius relation and tidal deformability, which are in a great harmony with current astronomical observations. The corresponding extrapolation uncertainty originates from the combined contributions of both the 264 optimal models and the linear regression on nuclear matter EOS, yielding a symmetry energy of $E\mathrm{_{sym}(5\rho_0)=136.0 \pm 52.8 MeV}$, a pressure of $P(5\rho_0) = 346.3 \pm 97.4 \mathrm{MeV/fm^{3}}$, a maximum neutron star mass of $M\mathrm{_{max}=2.18 \pm 0.18} M_{\odot}$, and a tidal deformability of $\Lambda_{1.4M_\odot} = 532 \pm 34$. This work establishes a general and data-driven framework to explore dense matter EOS by integrating \textit{ab initio} calculations with modern machine learning techniques.