VTNet: A multi-domain information fusion model for long-term multi-variate time series forecasting with application in irrigation water level

Time series forecasting is intricately tied to production and life, garnering widespread attention over an extended period. Enhancing the performance of long-term multivariate time series forecasting (MTSF) poses a highly challenging task, as it requires mining complicated and obscure temporal patterns in many aspects. For this reason, this paper proposes a long-term forecasting model based on multi-domain fusion (VTNet) to adaptively capture and refine multi-scale intra- and inter-variate dependencies. In contrast to previous techniques, we devise a dual-stream learning architecture. Firstly, the fast Fourier Transform (FFT) is adopted to extract frequency domain information. The original sequences are then transformed into 2D visual features in the temporal-frequency domain, and a 2D-TBlock is designed for multi-scale dynamic learning. Secondly, a combination of convolution and recurrent networks continues to explore the local temporal features and preserve the global trend. Finally, multi-modal circulant fusion is applied to achieve a more comprehensive and enriched feature fusion representation, further promoting overall performance. Extensive experiments are conducted on 9 public benchmark datasets and the real-world irrigation water level to showcase VTNet’s promoted performance and generalization. Moreover, VTNet yields 46.93% and 25.36% relative improvements for water level forecasting, revealing its potential application value in water-saving planning and extreme event early warning.