  Time series forecasting task predicts future trends based on historical
information. Transformer-based U-Net architectures, despite their success in
medical image segmentation, have limitations in both expressiveness and
computation efficiency in time series forecasting as evidenced in YFormer. To
tackle these challenges, we introduce Kernel-U-Net, a symmetric and
hierarchical U-shape neural network architecture. The kernel-U-Net encoder
compresses gradually input series into latent vectors, and its symmetric
decoder subsequently expands these vectors into output series. Specifically,
Kernel-U-Net separates the procedure of partitioning input time series into
patches from kernel manipulation, thereby providing the convenience of
executing customized kernels. Our method offers two primary advantages: 1)
Flexibility in kernel customization to adapt to specific datasets; 2) Enhanced
computational efficiency, with the complexity of the Transformer layer reduced
to linear. Experiments on seven real-world datasets, considering both
multivariate and univariate settings, demonstrate that Kernel-U-Net's
performance either exceeds or meets that of the existing state-of-the-art model
PatchTST in the majority of cases and outperforms Yformer. The source code for
Kernel-U-Net will be made publicly available for further research and
application.
