  Accurate forecasting of multivariate time series is an extensively studied
subject in finance, transportation, and computer science. Fully mining the
correlation and causation between the variables in a multivariate time series
exhibits noticeable results in improving the performance of a time series
model. Recently, some models have explored the dependencies between variables
through end-to-end graph structure learning without the need for predefined
graphs. However, current models do not incorporate the trade-off between
efficiency and flexibility and lack the guidance of domain knowledge in the
design of graph structure learning algorithms. This paper alleviates the above
issues by proposing Balanced Graph Structure Learning for Forecasting (BGSLF),
a novel deep learning model that joins graph structure learning and
forecasting. Technically, BGSLF leverages the spatial information into
convolutional operations and extracts temporal dynamics using the diffusion
convolutional recurrent network. The proposed framework balance the trade-off
between efficiency and flexibility by introducing Multi-Graph Generation
Network (MGN) and Graph Selection Module. In addition, a method named Smooth
Sparse Unit (SSU) is designed to sparse the learned graph structures, which
conforms to the sparse spatial correlations in the real world. Extensive
experiments on four real-world datasets demonstrate that our model achieves
state-of-the-art performances with minor trainable parameters. Code will be
made publicly available.
