# Physical Pooling Functions in Graph Neural Networks for Molecular Property Prediction

arXiv: https://arxiv.org/abs/2207.13779 · HTML: https://mlsanity.com/paper/2207.13779/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 60 references that are in the map.
- First posted on arXiv 27 Jul 2022.

## Builds on (most cited first, 22 of 22)

- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (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)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [Convolutional Networks on Graphs for Learning Molecular Fingerprints](https://mlsanity.com/paper/1509.09292/) (2015)
- [Directional Message Passing for Molecular Graphs](https://mlsanity.com/paper/2003.03123/) (2020)
- [Principal Neighbourhood Aggregation for Graph Nets](https://mlsanity.com/paper/2004.05718/) (2020)
- [Representation Learning on Graphs: Methods and Applications](https://mlsanity.com/paper/1709.05584/) (2017)
- [Analyzing Learned Molecular Representations for Property Prediction](https://mlsanity.com/paper/1904.01561/) (2019)
- [Learning Convolutional Neural Networks for Graphs](https://mlsanity.com/paper/1605.05273/) (2016)
- [Molecular Graph Convolutions: Moving Beyond Fingerprints](https://mlsanity.com/paper/1603.00856/) (2016)
- [Order Matters: Sequence to sequence for sets](https://mlsanity.com/paper/1511.06391/) (2015)
- [Molecular Property Prediction: A Multilevel Quantum Interactions Modeling Perspective](https://mlsanity.com/paper/1906.11081/) (2019)
- [Molecular Mechanics-Driven Graph Neural Network with Multiplex Graph for Molecular Structures](https://mlsanity.com/paper/2011.07457/) (2020)
- [Graph Neural Networks for Temperature-Dependent Activity Coefficient Prediction of Solutes in Ionic Liquids](https://mlsanity.com/paper/2206.11776/) (2022)
- [Gated Graph Recursive Neural Networks for Molecular Property Prediction](https://mlsanity.com/paper/1909.00259/) (2019)
- [Graph Machine Learning for Design of High-Octane Fuels](https://mlsanity.com/paper/2206.00619/) (2022)
- [Learning representations of molecules and materials with atomistic neural networks](https://mlsanity.com/paper/1812.04690/) (2018)

## Built on by (most cited first, 7 of 7)

- [Thermodynamics-Consistent Graph Neural Networks](https://mlsanity.com/paper/2407.18372/) (2024)
- [Generative AI and Process Systems Engineering: The Next Frontier](https://mlsanity.com/paper/2402.10977/) (2024)
- [Molecular Machine Learning in Chemical Process Design](https://mlsanity.com/paper/2508.20527/) (2025)
- [Integrating Chemical Language and Molecular Graph in Multimodal Fused Deep Learning for Drug Property Prediction](https://mlsanity.com/paper/2312.17495/) (2023)
- [Predicting the Temperature Dependence of Surfactant CMCs Using Graph Neural Networks](https://mlsanity.com/paper/2403.03767/) (2024)
- [SA-GAT-SR: Self-Adaptable Graph Attention Networks with Symbolic Regression for high-fidelity material property prediction](https://mlsanity.com/paper/2505.00625/) (2025)
- [A Systematic Evaluation of Molecular Mixture Behavior Prediction](https://mlsanity.com/paper/2605.29698/) (2026)

## Abstract (arXiv)

Graph neural networks (GNNs) are emerging in chemical engineering for the end-to-end learning of physicochemical properties based on molecular graphs. A key element of GNNs is the pooling function which combines atom feature vectors into molecular fingerprints. Most previous works use a standard pooling function to predict a variety of properties. However, unsuitable pooling functions can lead to unphysical GNNs that poorly generalize. We compare and select meaningful GNN pooling methods based on physical knowledge about the learned properties. The impact of physical pooling functions is demonstrated with molecular properties calculated from quantum mechanical computations. We also compare our results to the recent set2set pooling approach. We recommend using sum pooling for the prediction of properties that depend on molecular size and compare pooling functions for properties that are molecular size-independent. Overall, we show that the use of physical pooling functions significantly enhances generalization.