Differentiable Thermodynamic Phase-Equilibria for Machine Learning

Accurate prediction of phase equilibria remains a central challenge in chemical engineering. Physics-consistent machine learning methods that incorporate thermodynamic structure into neural networks have recently shown strong performance for activity-coefficient modeling. However, extending such approaches to equilibrium data arising from an extremum principle, such as liquid-liquid equilibria, remains difficult. Here we present DISCOMAX, a differentiable algorithm for phase-equilibrium calculation that guarantees thermodynamic consistency at both training and inference, only subject to a user-specified discretization. The method is rooted in statistical thermodynamics, and works via a discrete enumeration with subsequent masked softmax aggregation of feasible states, and together with a straight-through gradient estimator to enable physics-consistent end-to-end learning of neural $g^{E}$-models. We evaluate the approach on binary liquid-liquid equilibrium data and demonstrate that it outperforms existing surrogate-based methods, while offering a general framework for learning from different kinds of equilibrium data.