Four-dimensional QCD equation of state from a quasi-parton model with physics-informed neural networks

The equation of state (EoS) of strongly interacting matter at finite temperature and chemical potentials (baryon, charge, and strangeness) is a crucial input for hydrodynamic simulations of relativistic heavy-ion collisions. We construct a four-dimensional EoS using a deep-learning-assisted quasi-particle model (DLQPM) within a physics-informed neural network (PINN) framework, in which the masses of light quarks, strange quarks, and gluons are parameterized as functions of temperature and chemical potentials ($T, \mu_B, \mu_Q, \mu_S$). The model is constrained by lattice QCD data at vanishing chemical potentials and provides a thermodynamically consistent extrapolation to finite $\mu_{B,Q,S}$. The DLQPM accurately reproduces the lattice-calculated cumulants $\chi^{B,Q,S}_{i,j,k}$ at $\mu_{B,Q,S}=0$, and its predicted EoS at various chemical potentials agrees well with results from the generalized $T'$-expansion method in lattice QCD. Furthermore, the calculated baryon-strangeness correlation $C_{BS}$ is consistent, within uncertainties, with preliminary STAR data. This work offers a reliable EoS for exploring the QCD phase structure in the beam energy scan region.