# DeepEOSNet: Capturing the dependency on thermodynamic state in property prediction tasks

arXiv: https://arxiv.org/abs/2509.17018 · HTML: https://mlsanity.com/paper/2509.17018/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 37 references that are in the map.
- First posted on arXiv 21 Sep 2025.

## Builds on (most cited first, 20 of 20)

- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
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- [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)
- [SplitNets: Designing Neural Architectures for Efficient Distributed Computing on Head-Mounted Systems](https://mlsanity.com/paper/2204.04705/) (2022)
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- [SPT-NRTL: A physics-guided machine learning model to predict thermodynamically consistent activity coefficients](https://mlsanity.com/paper/2209.04135/) (2022)
- [PUFFIN: A Path-Unifying Feed-Forward Interfaced Network for Vapor Pressure Prediction](https://mlsanity.com/paper/2307.02903/) (2023)
- [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)
- [Predicting the Temperature-Dependent CMC of Surfactant Mixtures with Graph Neural Networks](https://mlsanity.com/paper/2411.02224/) (2024)
- [Graph Neural Networks embedded into Margules model for vapor-liquid equilibria prediction](https://mlsanity.com/paper/2502.18998/) (2025)

## Abstract (arXiv)

We propose a machine learning (ML) architecture to better capture the dependency of thermodynamic properties on the independent states. When predicting state-dependent thermodynamic properties, ML models need to account for both molecular structure and the thermodynamic state, described by independent variables, typically temperature, pressure, and composition. Modern molecular ML models typically include state information by adding it to molecular fingerprint vectors or by embedding explicit (semi-empirical) thermodynamic relations. Here, we propose to rather split the information processing on the molecular structure and the dependency on states into two separate network channels: a graph neural network and a multilayer perceptron, whose output is combined by a dot product. We refer to our approach as DeepEOSNet, as this idea is based on the DeepONet architecture [Lu et al. (2021), Nat. Mach. Intell.]: instead of operators, we learn state dependencies, with the possibility to predict equation of states (EOS). We investigate the predictive performance of DeepEOSNet by means of three case studies, which include the prediction of vapor pressure as a function of temperature, and mixture molar volume as a function of composition, temperature, and pressure. Our results show superior performance of DeepEOSNet for predicting vapor pressure and comparable performance for predicting mixture molar volume compared to state-of-research graph-based thermodynamic prediction models from our earlier works. In fact, we see large potential of DeepEOSNet in cases where data is sparse in the state domain and the output function is structurally similar across different molecules. The concept of DeepEOSNet can easily be transferred to other ML architectures in molecular context, and thus provides a viable option for property prediction.