Integrating neural networks with the 4D-TExS Model to classify stable and causal nuclear equations of state

Mapping the Quantum Chromodynamics (QCD) phase diagram behavior for the quark-gluon plasma state of matter and finding its critical point is still challenging in high-energy physics. Lattice QCD calculations at zero baryonic chemical potential have revealed a crossover transition from hadronic matter to a deconfined quark-gluon plasma state of matter. However, at finite chemical potential, the fermion sign problem is still present. Results from the Beam Energy Scan (BES) program at the Relativistic Heavy Ion Collider (RHIC) search for signatures of a first-order phase transition and a critical point at finite baryon chemical potential, providing constraints on the QCD Equation of State (EoS) and insights into the behavior of quark matter. We integrated the 4D-TExS Model based on a re-scaled temperature, with Utilities to Execute Pipelines (UTEP), enabling automated generation and a validation of EoS. This pipeline employs numerical differentiation to classify outputs as physically valid or invalid efficiently by conditions such as causality (0 < c_s² < 1) and stability (positive values for the pressure, entropy, and baryon density, the second-order baryon susceptibility, and the heat capacity). After validation, the workflow aims to develop and train a Neural Network to recognize pressure-based patterns and predict whether the output is valid without the need to compute numerical derivatives. Through this process, we reduce the computational cost and improve the precision of different models to generate EoS, enabling a more efficient analysis of the QCD phase diagram through computational physics and machine learning.