PatchTSFL: Patch Fourier Enhanced Linear for Long-Term Time-Series Forecasting

Long-term time series forecasting presents a critical challenge across numerous application domains. Recently, various transformer-based models have been employed for this task; however, these methods face two key challenges: difficulty in retaining local series information and failure to fully capture the overall trend of time series. To address these limitations, we propose a novel model called Patch Time Series Fourier-former Linear (PatchTSFL), which incorporates three innovative features: 1) A patching operation that splits long-term series into multiple patches, using the number of patches as the input length of the encoder, which preserves local sequence information while reducing model complexity; 2) A Fourier-enhanced block that replaces the traditional transformer’s multi-attention mechanism, capturing important information by converting time domain data into frequency domain mapping, further reducing computational complexity; 3) A Mixture Of Experts Decomposition block (MOEDecomp) that decomposes the series, enabling comprehensive capture of the overall time series trend. We conducted extensive experiments on nine widely-used long-term time series datasets, comparing PatchTSFL with state-of-the-art transformer-based models. Results demonstrate that PatchTSFL significantly improves forecasting accuracy (31.9% reduction in MSE and 19.0% reduction in MAE on average) while maintaining the lowest model complexity and runtime (4.3 times faster than FEDformer). These findings establish PatchTSFL as an effective and efficient solution for long-term time series prediction. The source code is available at: https://github.com/WESTBROOK-0/PatchTSFL.