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Physical Pooling Functions in Graph Neural Networks for Molecular Property Prediction

Artur M. Schweidtmann, Jan G. Rittig, Jana M. Weber, Martin Grohe, Manuel Dahmen, Kai Leonhard, Alexander Mitsos

TL;DR

This work demonstrates that the pooling function used to aggregate atomic representations into a molecular fingerprint in graph neural networks must align with the underlying physics of the target property. By contrasting sum, mean, max, and set2set pooling across 1-GNN and MXMNet architectures on QM9 and alkanes, the authors show that sum pooling reliably captures size-dependent (extensive) properties and improves extrapolation, while mean/max pooling can fail for such properties and sometimes overfit. For size-independent (intensive) properties, pooling choice is less critical, though certain combinations (e.g., mean or max) can outperform sum in extrapolation for some targets. Overall, incorporating physical insight into pooling choices yields better generalization and should guide pooling design in future GNN-based molecular-property predictions.

Abstract

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.

Physical Pooling Functions in Graph Neural Networks for Molecular Property Prediction

TL;DR

This work demonstrates that the pooling function used to aggregate atomic representations into a molecular fingerprint in graph neural networks must align with the underlying physics of the target property. By contrasting sum, mean, max, and set2set pooling across 1-GNN and MXMNet architectures on QM9 and alkanes, the authors show that sum pooling reliably captures size-dependent (extensive) properties and improves extrapolation, while mean/max pooling can fail for such properties and sometimes overfit. For size-independent (intensive) properties, pooling choice is less critical, though certain combinations (e.g., mean or max) can outperform sum in extrapolation for some targets. Overall, incorporating physical insight into pooling choices yields better generalization and should guide pooling design in future GNN-based molecular-property predictions.

Abstract

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.
Paper Structure (13 sections, 4 equations, 2 figures, 3 tables)

This paper contains 13 sections, 4 equations, 2 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Materials and methods
  3. Molecular graph
  4. Graph neural network
  5. Physical insight
  6. Results and discussion
  7. Hyperparameters and implementation
  8. Illustrative case study: Molecular weight
  9. Physicochemical properties
  10. Interpolation
  11. Generalization with 1-GNN architecture
  12. Generalization with MXMNet architecture
  13. Conclusion

Figures (2)

  • Figure 1: Illustration of the GNN structure highlighting the message passing and readout phases.
  • Figure 2: Mean absolute error in g/mol for test of the 1-GNN with different pooling functions, namely: sum, mean, max. (a) test data set of alkanes with up to 30 C-atoms, (b) external data set of alkanes with 35 up to 60 C-atoms. Results are for ten independent training runs, each with 500 periods.