# Thermodynamically consistent machine learning model for excess Gibbs energy

arXiv: https://arxiv.org/abs/2509.06484 · HTML: https://mlsanity.com/paper/2509.06484/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 63 references that are in the map.
- First posted on arXiv 8 Sep 2025.

## Builds on (most cited first, 12 of 12)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Convolutional Networks on Graphs for Learning Molecular Fingerprints](https://mlsanity.com/paper/1509.09292/) (2015)
- [ChemBERTa-2: Towards Chemical Foundation Models](https://mlsanity.com/paper/2209.01712/) (2022)
- [Learning Smooth Neural Functions via Lipschitz Regularization](https://mlsanity.com/paper/2202.08345/) (2022)
- [SELFormer: Molecular Representation Learning via SELFIES Language Models](https://mlsanity.com/paper/2304.04662/) (2023)
- [Gibbs-Duhem-Informed Neural Networks for Binary Activity Coefficient Prediction](https://mlsanity.com/paper/2306.07937/) (2023)
- [HANNA: Hard-constraint Neural Network for Consistent Activity Coefficient Prediction](https://mlsanity.com/paper/2407.18011/) (2024)
- [Gibbs-Helmholtz Graph Neural Network: capturing the temperature dependency of activity coefficients at infinite dilution](https://mlsanity.com/paper/2212.01199/) (2022)
- [Thermodynamics-Consistent Graph Neural Networks](https://mlsanity.com/paper/2407.18372/) (2024)
- [SPT-NRTL: A physics-guided machine learning model to predict thermodynamically consistent activity coefficients](https://mlsanity.com/paper/2209.04135/) (2022)
- [Advancing Thermodynamic Group-Contribution Methods by Machine Learning: UNIFAC 2.0](https://mlsanity.com/paper/2408.05220/) (2024)

## Built on by (most cited first, 3 of 3)

- [Blind Thermodynamic Ontology Discovery from Anonymous Experiments](https://mlsanity.com/paper/2609.23387/) (2026)
- [Predicting Activities in Aqueous Electrolyte Solutions with Hybrid Machine Learning](https://mlsanity.com/paper/2607.19114/) (2026)
- [Atoms to Processes: The Role of Artificial Intelligence and Machine Learning in Chemical Engineering](https://mlsanity.com/paper/2610.02014/) (2026)

## Abstract (arXiv)

The excess Gibbs energy plays a central role in chemical engineering and chemistry, providing a basis for modeling thermodynamic properties of liquid mixtures. Predicting the excess Gibbs energy of multi-component mixtures solely from molecular structures is a long-standing challenge. We address this challenge with HANNA, a flexible machine learning model for excess Gibbs energy that integrates physical laws as hard constraints, guaranteeing thermodynamically consistent predictions. HANNA is trained on experimental data for vapor-liquid equilibria, liquid-liquid equilibria, activity coefficients at infinite dilution and excess enthalpies in binary mixtures. The end-to-end training on liquid-liquid equilibrium data is facilitated by a surrogate solver. A geometric projection method enables robust extrapolations to multi-component mixtures. We demonstrate that HANNA delivers accurate predictions, while providing a substantially broader domain of applicability than state-of-the-art benchmark methods. The trained model and corresponding code are openly available, and an interactive interface is provided on our website, MLPROP.