Density functional theory (DFT) is the most successful and widely used approach for computing the electronic structure of matter. However, for tasks involving large sets of candidate molecules, running DFT separately for every possible compound of interest is forbiddingly expensive. In this paper, we propose a neural network based machine learning algorithm which, assuming a sufficiently large training sample of actual DFT results, can instead learn to predict certain properties of molecules purely from their molecular graphs. Our algorithm is based on the recently proposed covariant compositional networks framework and involves tensor reduction operations that are covariant with respect to permutations of the atoms. This new approach avoids some of the representational limitations of other neural networks that are popular in learning from molecular graphs and yields promising results in numerical experiments on the Harvard Clean Energy Project and QM9 molecular datasets.
Contemporary graph learning algorithms are not well-suited for large molecules since they do not consider the hierarchical interactions among the atoms, which are essential to determining the molecular properties of macromolecules. In this work, we propose Multiresolution Graph Transformers (MGT), the first graph transformer architecture that can learn to represent large molecules at multiple scales. MGT can learn to produce representations for the atoms and group them into meaningful functional groups or repeating units. We also introduce Wavelet Positional Encoding (WavePE), a new positional encoding method that can guarantee localization in both spectral and spatial domains. Our proposed model achieves competitive results on three macromolecule datasets consisting of polymers, peptides, and protein-ligand complexes, along with one drug-like molecule dataset. Significantly, our model outperforms other state-of-the-art methods and achieves chemical accuracy in estimating molecular properties (e.g., highest occupied molecular orbital, lowest unoccupied molecular orbital, and their gap) calculated by Density Functional Theory in the polymers dataset. Furthermore, the visualizations, including clustering results on macromolecules and low-dimensional spaces of their representations, demonstrate the capability of our methodology in learning to represent long-range and hierarchical structures. Our PyTorch implementation is publicly available at https://github.com/HySonLab/Multires-Graph-Transformer.
In this paper, we propose Multiresolution Equivariant Graph Variational Autoencoders (MGVAE), the first hierarchical generative model to learn and generate graphs in a multiresolution and equivariant manner. At each resolution level, MGVAE employs higher order message passing to encode the graph while learning to partition it into mutually exclusive clusters and coarsening into a lower resolution that eventually creates a hierarchy of latent distributions. MGVAE then constructs a hierarchical generative model to variationally decode into a hierarchy of coarsened graphs. Importantly, our proposed framework is end-to-end permutation equivariant with respect to node ordering. MGVAE achieves competitive results with several generative tasks including general graph generation, molecular generation, unsupervised molecular representation learning to predict molecular properties, link prediction on citation graphs, and graph-based image generation. Our implementation is available at https://github.com/HyTruongSon/MGVAE.
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