# SPT-NRTL: A physics-guided machine learning model to predict thermodynamically consistent activity coefficients

arXiv: https://arxiv.org/abs/2209.04135 · HTML: https://mlsanity.com/paper/2209.04135/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 49 references that are in the map.
- First posted on arXiv 9 Sep 2022.

## Builds on (most cited first, 9 of 9)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Molecular Transformer - A Model for Uncertainty-Calibrated Chemical Reaction Prediction](https://mlsanity.com/paper/1811.02633/) (2018)
- [SMILES Transformer: Pre-trained Molecular Fingerprint for Low Data Drug Discovery](https://mlsanity.com/paper/1911.04738/) (2019)
- [Generative Chemical Transformer: Neural Machine Learning of Molecular Geometric Structures from Chemical Language via Attention](https://mlsanity.com/paper/2103.00213/) (2021)
- [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)
- [Predicting Chemical Properties using Self-Attention Multi-task Learning based on SMILES Representation](https://mlsanity.com/paper/2010.11272/) (2020)

## Built on by (most cited first, 11 of 11)

- [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)
- [Thermodynamics-Consistent Graph Neural Networks](https://mlsanity.com/paper/2407.18372/) (2024)
- [PUFFIN: A Path-Unifying Feed-Forward Interfaced Network for Vapor Pressure Prediction](https://mlsanity.com/paper/2307.02903/) (2023)
- [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)
- [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)
- [Data-Driven Extended Corresponding State Approach for Residual Property Prediction of Hydrofluoroolefins](https://mlsanity.com/paper/2507.21720/) (2025)
- [DeepEOSNet: Capturing the dependency on thermodynamic state in property prediction tasks](https://mlsanity.com/paper/2509.17018/) (2025)

## Abstract (arXiv)

The availability of property data is one of the major bottlenecks in the development of chemical processes, often requiring time-consuming and expensive experiments or limiting the design space to a small number of known molecules. This bottleneck has been the motivation behind the continuing development of predictive property models. For the property prediction of novel molecules, group contribution methods have been groundbreaking. In recent times, machine learning has joined the more established property prediction models. However, even with recent successes, the integration of physical constraints into machine learning models remains challenging. Physical constraints are vital to many thermodynamic properties, such as the Gibbs-Duhem relation, introducing an additional layer of complexity into the prediction. Here, we introduce SPT-NRTL, a machine learning model to predict thermodynamically consistent activity coefficients and provide NRTL parameters for easy use in process simulations. The results show that SPT-NRTL achieves higher accuracy than UNIFAC in the prediction of activity coefficients across all functional groups and is able to predict many vapor-liquid-equilibria with near experimental accuracy, as illustrated for the exemplary mixtures water/ethanol and chloroform/n-hexane. To ease the application of SPT-NRTL, NRTL-parameters of 100 000 000 mixtures are calculated with SPT-NRTL and provided online.