Abstract: Gas state equations play an important role in thermodynamic modeling and engineering applications. Although cubic state equations such as Redlich Kwong Soave (RKS) and Peng Robinson (PR) are widely used due to their concise form and easily obtainable parameters, their prediction accuracy significantly decreases under under high-temperature and high-pressure conditions or when dealing with polar fluids such as water vapor. To enhance its generalization capability, physics-informed neural network model (PINN) are employed here to develop a state equation correction and optimization model by using water vapor as the working fluid. Specifically, we introduced a high-order volume term (proportional to ρ³) in the RKS and PR equation expressions to enhance their ability to describe complex intermolecular forces. The core of this study involves employing Physics-Informed Neural Networks (PINN) to embed the equation of state (EOS) itself, along with critical point constraints, as physical regularizers within the machine learning framework. By integrating extensive datasets of saturated vapor-liquid properties experimental data, the model's high-order coefficients are optimized through a hybrid data-driven and physics-based approach. This methodology culminates in a novel EOS-PINN predictive model with a robust physical foundation. Compared to the original RKS and PR state equations, the predictive accuracy of the EOS-PINN model has improved by 7.775% and 4.33%, respectively. In particular, their prediction errors were reduced to 0.93% and 1.63% in the gas phase region, respectively. Graphical analyses of the predicted isotherms confirm the model's strict adherence to thermodynamic consistency, notably satisfying Maxwell's equal-area rule. This approach effectively circumvents the physical inconsistencies inherent in purely data-driven models. Consequently, this study establishes a effective paradigm for fusing physical laws with machine learning to advance the development of a new generation of intelligent thermodynamic models.