Exploring the Hierarchical Sparsity in Long-Term Multivariate Energy Data for Effective and Efficient Forecasting

Energy forecasting plays a vital role in smart grid technology frameworks for monitoring power systems, including energy generation and consumption systems. As a downstream task of time series forecasting, energy forecasting has been thoroughly studied on the basis of deep learning in recent years. However, the sparsity of multivariate energy data, as well as the sparsity involved in cases with multiple solutions, has received minimal attention. To fill this gap, this work analyzes the intra-series and inter-series sparsity of long-term multivariate energy data in a hierarchical manner. Specifically, hierarchical global time stamps are leveraged to represent intra-series sparsity. Moreover, wavelet theory is applied to identify inter-series sparsity according to the correlations of series at different frequency scales. Building upon the above analysis of hierarchical sparsity, this work presents a novel energy forecasting model, the hierarchically sparse transformer, which uses a novel pyramid architecture to hierarchically extract sparse intra-series and inter-series features for effective and efficient energy forecasting. Extensive experiments on four energy-related benchmarks demonstrate the state-of-the-art performance of the proposed model. The source code is released on https://github.com/OrigamiSL/HST.