Differentiable Thermodynamic Phase-Equilibria for Machine Learning

2026-03-11

AI Summary

Accurately predicting phase equilibria—such as liquid–liquid equilibrium—remains a central challenge in chemical engineering thermodynamics, and existing machine learning approaches struggle to enforce thermodynamic consistency while incorporating the principle of thermodynamic extremum. This work proposes DISCOMAX, a differentiable algorithm for phase equilibrium computation that, for the first time, enables end-to-end training of neural excess Gibbs free energy (g^E) models while rigorously satisfying thermodynamic consistency. By integrating statistical thermodynamics–based discrete state enumeration, masked softmax aggregation, and a straight-through gradient estimator, the framework is both general and physically principled. It unifies the treatment of diverse phase equilibrium data and outperforms existing surrogate models on binary liquid–liquid equilibrium tasks without compromising physical correctness.

Technology Category

Machine Learning: Graph-based Machine LearningSearch and Optimization: Mixed Discrete/Continuous SearchConstraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphsSemantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semanticsSearch and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

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.

Problem

• phase equilibria
• liquid-liquid equilibria
• thermodynamic consistency
• machine learning
• chemical engineering

Innovation

• differentiable phase equilibrium
• thermodynamic consistency
• DISCOMAX
• neural g^E models
• masked softmax aggregation