Abstract
Activity coefficients are key thermodynamic quantities for describing phase equilibria, but their experimental determination entails laborious and costly phase-equilibrium measurements, making predictive approaches highly desirable. The potential of machine learning for such predictions has received growing attention as an alternative to physics-based models that require experimental data or expensive calculations for parameterization. We propose a physics-informed edge-enhanced graph attention network (PEGAT) to predict activity coefficients in multicomponent mixtures, where each molecule is encoded as a graph in which the nodes correspond to atoms and the edges to chemical bonds. The excess Gibbs free energy of the mixture is predicted using the proposed model, including a nonlinear transformation in the final layer to ensure that the excess Gibbs free energy vanishes for pure components. To further enforce thermodynamic consistency, the relevant activity coefficients are obtained via the Gibbs-Duhem relation. Unlike machine-learning models developed primarily for binary systems, the proposed framework is directly applicable to arbitrary multicomponent mixtures. The PEGAT model is evaluated using a mixed dataset comprising both binary and ternary mixture data and demonstrates high predictive accuracy. Further validation on representative mixtures shows close agreement between predicted and reference activity coefficients. The results confirm that improved thermodynamic consistency can be achieved by embedding hard physical constraints into the graph neural network architecture. However, they also highlight that unphysical behaviors may still be predicted despite these constraints.