# Gibbs-Helmholtz Graph Neural Network: capturing the temperature dependency of activity coefficients at infinite dilution

arXiv: https://arxiv.org/abs/2212.01199 · HTML: https://mlsanity.com/paper/2212.01199/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 59 references that are in the map.
- First posted on arXiv 2 Dec 2022.

## Builds on (most cited first, 16 of 16)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014)
- [Analyzing Learned Molecular Representations for Property Prediction](https://mlsanity.com/paper/1904.01561/) (2019)
- [GraphNorm: A Principled Approach to Accelerating Graph Neural Network Training](https://mlsanity.com/paper/2009.03294/) (2020)
- [Machine Learning in Thermodynamics: Prediction of Activity Coefficients by Matrix Completion](https://mlsanity.com/paper/2001.10675/) (2020)
- [A smile is all you need: Predicting limiting activity coefficients from SMILES with natural language processing](https://mlsanity.com/paper/2206.07048/) (2022)
- [Graph Neural Networks for Temperature-Dependent Activity Coefficient Prediction of Solutes in Ionic Liquids](https://mlsanity.com/paper/2206.11776/) (2022)
- [Hybridizing Physical and Data-driven Prediction Methods for Physicochemical Properties](https://mlsanity.com/paper/2202.08804/) (2022)

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

- [Thermodynamics-Consistent Graph Neural Networks](https://mlsanity.com/paper/2407.18372/) (2024)
- [GraphXForm: Graph transformer for computer-aided molecular design](https://mlsanity.com/paper/2411.01667/) (2024)
- [GRAPPA -- A Hybrid Graph Neural Network for Predicting Pure Component Vapor Pressures](https://mlsanity.com/paper/2501.08729/) (2025)
- [Tabular foundation models for in-context prediction of molecular properties](https://mlsanity.com/paper/2604.16123/) (2026)
- [Molecular Machine Learning in Chemical Process Design](https://mlsanity.com/paper/2508.20527/) (2025)
- [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)
- [Predicting the Temperature Dependence of Surfactant CMCs Using Graph Neural Networks](https://mlsanity.com/paper/2403.03767/) (2024)
- [DeepEOSNet: Capturing the dependency on thermodynamic state in property prediction tasks](https://mlsanity.com/paper/2509.17018/) (2025)
- [A Systematic Evaluation of Molecular Mixture Behavior Prediction](https://mlsanity.com/paper/2605.29698/) (2026)

## Abstract (arXiv)

The accurate prediction of physicochemical properties of chemical compounds in mixtures (such as the activity coefficient at infinite dilution γij^∞) is essential for developing novel and more sustainable chemical processes. In this work, we analyze the performance of previously-proposed GNN-based models for the prediction of γij^∞, and compare them with several mechanistic models in a series of 9 isothermal studies. Moreover, we develop the Gibbs-Helmholtz Graph Neural Network (GH-GNN) model for predicting ln γij^∞ of molecular systems at different temperatures. Our method combines the simplicity of a Gibbs-Helmholtz-derived expression with a series of graph neural networks that incorporate explicit molecular and intermolecular descriptors for capturing dispersion and hydrogen bonding effects. We have trained this model using experimentally determined ln γij^∞ data of 40,219 binary-systems involving 1032 solutes and 866 solvents, overall showing superior performance compared to the popular UNIFAC-Dortmund model. We analyze the performance of GH-GNN for continuous and discrete inter/extrapolation and give indications for the model's applicability domain and expected accuracy. In general, GH-GNN is able to produce accurate predictions for extrapolated binary-systems if at least 25 systems with the same combination of solute-solvent chemical classes are contained in the training set and a similarity indicator above 0.35 is also present. This model and its applicability domain recommendations have been made open-source at https://github.com/edgarsmdn/GH-GNN.