[Paper Review] Directional Message Passing for Molecular Graphs

Johannes Gasteiger, Janek Groß+1 more|arXiv (Cornell University)|Mar 6, 2020

Computational Drug Discovery Methods345 citations

TL;DR

DimeNet introduces directional message passing with spherical Fourier-Bessel bases to encode distances and angles between atoms, achieving state-of-the-art molecular property predictions and enabling smooth, differentiable force predictions for MD.

ABSTRACT

Graph neural networks have recently achieved great successes in predicting quantum mechanical properties of molecules. These models represent a molecule as a graph using only the distance between atoms (nodes). They do not, however, consider the spatial direction from one atom to another, despite directional information playing a central role in empirical potentials for molecules, e.g. in angular potentials. To alleviate this limitation we propose directional message passing, in which we embed the messages passed between atoms instead of the atoms themselves. Each message is associated with a direction in coordinate space. These directional message embeddings are rotationally equivariant since the associated directions rotate with the molecule. We propose a message passing scheme analogous to belief propagation, which uses the directional information by transforming messages based on the angle between them. Additionally, we use spherical Bessel functions and spherical harmonics to construct theoretically well-founded, orthogonal representations that achieve better performance than the currently prevalent Gaussian radial basis representations while using fewer than 1/4 of the parameters. We leverage these innovations to construct the directional message passing neural network (DimeNet). DimeNet outperforms previous GNNs on average by 76% on MD17 and by 31% on QM9. Our implementation is available online.

Motivation & Objective

• Incorporate directional information into GNNs to capture angular and torsional effects in molecules.
• Develop principled, orthogonal basis representations for distances and angles using spherical Bessel functions and spherical harmonics.
• Propose the DimeNet architecture to predict molecular properties and enable energy-conserving molecular dynamics simulations.

Proposed method

• Embed messages as directional embeddings associated with atom pairs rather than atom centers.
• Represent distances with radial basis functions and angles with a 2D spherical Fourier-Bessel basis.
• Update and aggregate directional message embeddings in an analogy to belief propagation with angle- and distance-dependent interactions.
• Ensure rotational, translational, permutation, and inversion invariances; enable continuous differentiability for MD.

Experimental results

Research questions

• RQ1 How can directional information (angles between neighbor directions) be integrated into GNNs for molecules?
• RQ2 Do spherical Bessel and spherical harmonics bases improve efficiency and accuracy for representing interatomic distances/angles?
• RQ3 Can a GNN with directional message passing set new state-of-the-art on QM9 and MD17 benchmarks?

Key findings

• DimeNet outperforms prior GNNs by 76% on MD17 and 31% on QM9 on average.
• Using spherical Bessel basis representations reduces parameter count while improving performance compared to Gaussian radial bases.
• Ablation shows that directional information and the 2D spherical Fourier-Bessel basis substantially impact performance (e.g., NSHBF=1 degrades MAE; removing directional messages severely harms results).
• DimeNet achieves state-of-the-art performance on 11 of 12 QM9 targets and provides competitive MD results with 1000 training samples.
• The model is twice continuously differentiable and suitable for predicting both energies and atomic forces, enabling energy-conserving MD simulations.