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The Transformer architecture has become a dominant choice in many domains, such as natural language processing and computer vision. Yet, it has not achieved competitive performance on popular leaderboards of graph-level prediction compared to mainstream GNN variants. Therefore, it remains a mystery how Transformers could perform well for graph representation learning. In this paper, we solve this mystery by presenting Graphormer, which is built upon the standard Transformer architecture, and could attain excellent results on a broad range of graph representation learning tasks, especially on the recent OGB Large-Scale Challenge. Our key insight to utilizing Transformer in the graph is the necessity of effectively encoding the structural information of a graph into the model. To this end, we propose several simple yet effective structural encoding methods to help Graphormer better model graph-structured data. Besides, we mathematically characterize the expressive power of Graphormer and exhibit that with our ways of encoding the structural information of graphs, many popular GNN variants could be covered as the special cases of Graphormer. The code and models of Graphormer will be made publicly available at https://github.com/Microsoft/Graphormer.

Efficient prediction of the air quality response to emission changes is a prerequisite for an integrated assessment system in developing effective control policies. Yet, representing the nonlinear response of air quality to emission controls with accuracy remains a major barrier in air quality-related decision making. Here, we demonstrate a novel method that combines deep learning approaches with chemical indicators of pollutant formation to quickly estimate the coefficients of air quality response functions using ambient concentrations of 18 chemical indicators simulated with a comprehensive atmospheric chemical transport model (CTM). By requiring only two CTM simulations for model application, the new method significantly enhances the computational efficiency compared to existing methods that achieve lower accuracy despite requiring 20+ CTM simulations (the benchmark statistical model). Our results demonstrate the utility of deep learning approaches for capturing the nonlinearity of atmospheric chemistry and physics and the prospects of the new method to support effective policymaking in other environment systems.

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