# Thermodynamics-Consistent Graph Neural Networks

arXiv: https://arxiv.org/abs/2407.18372 · HTML: https://mlsanity.com/paper/2407.18372/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 38 references that are in the map.
- First posted on arXiv 8 Jul 2024.

## Builds on (most cited first, 11 of 11)

- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Graph neural networks for materials science and chemistry](https://mlsanity.com/paper/2208.09481/) (2022)
- [A smile is all you need: Predicting limiting activity coefficients from SMILES with natural language processing](https://mlsanity.com/paper/2206.07048/) (2022)
- [Gibbs-Duhem-Informed Neural Networks for Binary Activity Coefficient Prediction](https://mlsanity.com/paper/2306.07937/) (2023)
- [Graph Neural Networks for Temperature-Dependent Activity Coefficient Prediction of Solutes in Ionic Liquids](https://mlsanity.com/paper/2206.11776/) (2022)
- [Graph neural networks for the prediction of molecular structure-property relationships](https://mlsanity.com/paper/2208.04852/) (2022)
- [Gibbs-Helmholtz Graph Neural Network: capturing the temperature dependency of activity coefficients at infinite dilution](https://mlsanity.com/paper/2212.01199/) (2022)
- [SPT-NRTL: A physics-guided machine learning model to predict thermodynamically consistent activity coefficients](https://mlsanity.com/paper/2209.04135/) (2022)
- [Physical Pooling Functions in Graph Neural Networks for Molecular Property Prediction](https://mlsanity.com/paper/2207.13779/) (2022)
- [Balancing Molecular Information and Empirical Data in the Prediction of Physico-Chemical Properties](https://mlsanity.com/paper/2406.08075/) (2024)
- [Learning representations of molecules and materials with atomistic neural networks](https://mlsanity.com/paper/1812.04690/) (2018)

## Built on by (most cited first, 12 of 12)

- [HANNA: Hard-constraint Neural Network for Consistent Activity Coefficient Prediction](https://mlsanity.com/paper/2407.18011/) (2024)
- [GraphXForm: Graph transformer for computer-aided molecular design](https://mlsanity.com/paper/2411.01667/) (2024)
- [Molecular Machine Learning in Chemical Process Design](https://mlsanity.com/paper/2508.20527/) (2025)
- [Hierarchical Matrix Completion for the Prediction of Properties of Binary Mixtures](https://mlsanity.com/paper/2410.06060/) (2024)
- [Predicting the Temperature-Dependent CMC of Surfactant Mixtures with Graph Neural Networks](https://mlsanity.com/paper/2411.02224/) (2024)
- [Federated Learning from Molecules to Processes: A Perspective](https://mlsanity.com/paper/2506.18525/) (2025)
- [Thermodynamically consistent machine learning model for excess Gibbs energy](https://mlsanity.com/paper/2509.06484/) (2025)
- [Graph Neural Networks embedded into Margules model for vapor-liquid equilibria prediction](https://mlsanity.com/paper/2502.18998/) (2025)
- [Differentiable Thermodynamic Phase-Equilibria for Machine Learning](https://mlsanity.com/paper/2603.11249/) (2026)
- [DeepEOSNet: Capturing the dependency on thermodynamic state in property prediction tasks](https://mlsanity.com/paper/2509.17018/) (2025)
- [Clapeyron Neural Networks for Single-Species Vapor-Liquid Equilibria](https://mlsanity.com/paper/2602.18313/) (2026)
- [A Systematic Evaluation of Molecular Mixture Behavior Prediction](https://mlsanity.com/paper/2605.29698/) (2026)

## Abstract (arXiv)

We propose excess Gibbs free energy graph neural networks (GE-GNNs) for predicting composition-dependent activity coefficients of binary mixtures. The GE-GNN architecture ensures thermodynamic consistency by predicting the molar excess Gibbs free energy and using thermodynamic relations to obtain activity coefficients. As these are differential, automatic differentiation is applied to learn the activity coefficients in an end-to-end manner. Since the architecture is based on fundamental thermodynamics, we do not require additional loss terms to learn thermodynamic consistency. As the output is a fundamental property, we neither impose thermodynamic modeling limitations and assumptions. We demonstrate high accuracy and thermodynamic consistency of the activity coefficient predictions.