Neural message passing algorithms for semi-supervised classification on graphs have recently achieved great success. However, for classifying a node these methods only consider nodes that are a few propagation steps away and the size of this utilized neighborhood is hard to extend. In this paper, we use the relationship between graph convolutional networks (GCN) and PageRank to derive an improved propagation scheme based on personalized PageRank. We utilize this propagation procedure to construct a simple model, personalized propagation of neural predictions (PPNP), and its fast approximation, APPNP. Our model's training time is on par or faster and its number of parameters on par or lower than previous models. It leverages a large, adjustable neighborhood for classification and can be easily combined with any neural network. We show that this model outperforms several recently proposed methods for semi-supervised classification in the most thorough study done so far for GCN-like models. Our implementation is available online. 1
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. 1
Graph neural networks (GNNs) have emerged as a powerful machine learning approach for the prediction of molecular properties. In particular, recently proposed advanced GNN models promise quantum chemical accuracy at a fraction of the computational cost. While the capabilities of such advanced GNNs have been extensively demonstrated on benchmark datasets, there have been few applications in real atomistic simulations. Here, we therefore put the robustness of GNN interatomic potentials to the test, using the recently proposed GemNet architecture as a testbed. Models are trained on the QM7-x database of organic molecules and used to perform extensive MD simulations. We find that low test set errors are not sufficient for obtaining stable dynamics and that severe pathologies sometimes only become apparent after hundreds of ps of dynamics. Nonetheless, highly stable and transferable GemNet potentials can be obtained with sufficiently large training sets.
Effectively predicting molecular interactions has the potential to accelerate molecular dynamics by multiple orders of magnitude and thus revolutionize chemical simulations. Graph neural networks (GNNs) have recently shown great successes for this task, overtaking classical methods based on fixed molecular kernels. However, they still appear very limited from a theoretical perspective, since regular GNNs cannot distinguish certain types of graphs. In this work we close this gap between theory and practice. We show that GNNs with directed edge embeddings and two-hop message passing are indeed universal approximators for predictions that are invariant to global rotation and translation, and equivariant to permutation. We then leverage these insights and multiple structural improvements to propose the geometric message passing neural network (GemNet). We demonstrate the benefits of the proposed changes in multiple ablation studies. GemNet outperforms previous models on the COLL and MD17 molecular dynamics datasets by 34 % and 40 %, performing especially well on the most challenging molecules.Preprint. Under review.
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