Accurately constructing the Equation of State (EoS) for Quantum Chromodynamics (QCD) matter in the region with finite baryon chemical potential (μB) is a central challenge in modern high-energy nuclear physics research.

This study aims to address this challenge and explore the QCD phase diagram structure and locate the critical endpoint.

First, the study constructed three deep neural networks to achieve high-precision reconstruction of the QCD EoS at zero μB. Then, we analyzed the monotonic behavior of the fourth-order generalized susceptibility χ4B at different temperatures T and μB, and calculated the dependence of the fourth-order cumulant ratio R42 on collision energy sNN.

We have estimated the possible location of the QCD critical endpoint (CEP) as (T, μB) = ((0.113±0.019) GeV, (0.634±0.11) GeV). The results for the fourth-order cumulant ratio R42 not only match the experimental data well but also show significant fluctuation behavior near 6 GeV.

The deep-learning quasi-parton model provides a self-consistent theoretical framework for studying the thermodynamic and transport properties of QCD matter at finite baryon density. The obtained EoS parameters can be directly applied to hydrodynamic simulations for the beam energy scan program of the Relativistic Heavy Ion Collider (RHIC), offering a new research tool for exploring the QCD phase diagram structure and searching for CEP.