multivariate time series imputation with graph neural network based on the physics laws.

What is it about?

find the missing data in multivariate time series by the graph neural network with a better explainability from the physics law. This can help us know about the data potiential structure and physics law behind the dataset. We use the transportation, air pollution and electricity to test our model and find out the missing data.

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Why is it important?

we propose a novel higher-order spatio-temporal physics-incorporated GNN (HSPGNN). Firstly, the dynamic Laplacian matrix can be obtained by the spatial attention mechanism. Then, the generic inhomogeneous partial differential equation (PDE) of physical dynamic systems is used to construct the dynamic higher-order spatio-temporal GNN adaptively to obtain the missing time series values. Moreover, we estimate the missing impact by Normalizing Flows (NF) to evaluate the importance of each node in the graph for better explainability. Experimental re- sults on four benchmark datasets demonstrate the effectiveness of HSPGNN and the superior performance when combining various order neighbor nodes. Also, graph-like optical flow, dynamic graphs, and missing impact can be obtained naturally by HSPGNN, which provides better dynamic analysis and explanation than traditional data-driven models.

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