Differentiable Thermodynamic Phase-Equilibria for Machine Learning.

Authors

Karim K Ben Hicham, Moreno Ascani, Jan G Rittig, Alexander Mitsos

Published in

Journal of chemical information and modeling. Volume 66. Issue 17. Pages 10487-10502. Sep 14, 2026.

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 combines discrete enumeration of feasible phase states with masked softmax aggregation in the backward pass, with the propagation of the true equilibrium state in the forward pass, using a straight-through gradient estimator to enable physics-consistent end-to-end learning of neural excess Gibbs energy (gE)-models. We show that this approach bears analogy to statistical thermodynamics, and we evaluate it on binary liquid-liquid equilibrium data where it outperforms existing surrogate-based methods, while offering a general framework for learning from different kinds of equilibrium data.

PMID:
42734501
Bibliographic data and abstract were imported from PubMed on 14 Sep 2026.

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