# Gibbs-Duhem-Informed Neural Networks for Binary Activity Coefficient Prediction

arXiv: https://arxiv.org/abs/2306.07937 · HTML: https://mlsanity.com/paper/2306.07937/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 45 references that are in the map.
- First posted on arXiv 31 May 2023.

## Builds on (most cited first, 7 of 7)

- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Neural Collaborative Filtering](https://mlsanity.com/paper/1708.05031/) (2017)
- [Graph neural networks for materials science and chemistry](https://mlsanity.com/paper/2208.09481/) (2022)
- [Thermodynamics-informed graph neural networks](https://mlsanity.com/paper/2203.01874/) (2022)
- [Machine Learning in Thermodynamics: Prediction of Activity Coefficients by Matrix Completion](https://mlsanity.com/paper/2001.10675/) (2020)
- [Graph Neural Networks for Temperature-Dependent Activity Coefficient Prediction of Solutes in Ionic Liquids](https://mlsanity.com/paper/2206.11776/) (2022)
- [SPT-NRTL: A physics-guided machine learning model to predict thermodynamically consistent activity coefficients](https://mlsanity.com/paper/2209.04135/) (2022)

## Built on by (most cited first, 17 of 17)

- [HANNA: Hard-constraint Neural Network for Consistent Activity Coefficient Prediction](https://mlsanity.com/paper/2407.18011/) (2024)
- [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)
- [Molecular Machine Learning in Chemical Process Design](https://mlsanity.com/paper/2508.20527/) (2025)
- [Graph Neural Networks for Surfactant Multi-Property Prediction](https://mlsanity.com/paper/2401.01874/) (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)
- [Predicting the Temperature Dependence of Surfactant CMCs Using Graph Neural Networks](https://mlsanity.com/paper/2403.03767/) (2024)
- [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)
- [MultiPUFFIN: A Multimodal Domain-Constrained Foundation Model for Molecular Property Prediction of Small Molecules](https://mlsanity.com/paper/2603.00857/) (2026)
- [A Systematic Evaluation of Molecular Mixture Behavior Prediction](https://mlsanity.com/paper/2605.29698/) (2026)
- [Chem World: A Large-Scale Benchmark and Physics-Informed Framework for Trustworthy Chemical Property Prediction](https://mlsanity.com/paper/2607.28079/) (2026)

## Abstract (arXiv)

We propose Gibbs-Duhem-informed neural networks for the prediction of binary activity coefficients at varying compositions. That is, we include the Gibbs-Duhem equation explicitly in the loss function for training neural networks, which is straightforward in standard machine learning (ML) frameworks enabling automatic differentiation. In contrast to recent hybrid ML approaches, our approach does not rely on embedding a specific thermodynamic model inside the neural network and corresponding prediction limitations. Rather, Gibbs-Duhem consistency serves as regularization, with the flexibility of ML models being preserved. Our results show increased thermodynamic consistency and generalization capabilities for activity coefficient predictions by Gibbs-Duhem-informed graph neural networks and matrix completion methods. We also find that the model architecture, particularly the activation function, can have a strong influence on the prediction quality. The approach can be easily extended to account for other thermodynamic consistency conditions.