A Multi-Stage Graph Neural Network–Physics-Informed Neural Network (GNN–PINN) Framework for Thermodynamic Property Prediction

Accurately predicting thermodynamic properties across various conditions remains a critical challenge, particularly in scenarios involving sparse data or complex molecular interactions. This study proposes a multistage hybrid modeling framework that integrates Graph Neural Networks (GNN) and Physics-Informed Neural Networks (PINN) to predict essential thermodynamic properties, including enthalpy and entropy, for pure substances under various conditions. The model is developed in three distinct stages. First, a GNN encoder captures atomic-level interactions (both bonded and nonbonded) from molecular structures, generating structurally enriched molecular embeddings while leveraging critical constants and reduced state variables through a masking strategy that enables learning from single-phase data sets. Second, a regression submodel utilizes these embeddings to accurately predict saturation pressure (P^sat) from molecular structure and temperature, modeling phase equilibrium behavior. Finally, the third stage employs PINN-based fine-tuning, embedding thermodynamic constraints─such as Gibbs free energy equality at phase equilibrium and enthalpy–entropy coupling─as penalties in the loss function to enforce thermodynamic consistency. This integrated GNN–PINN approach accurately predicts vapor- and liquid-phase enthalpies, entropies, and saturation pressures, maintaining robust performance even at equilibrium conditions. The model offers a physically consistent and reliable method for predicting thermodynamic properties, effectively capturing complex molecular interactions while adhering to fundamental physical laws.