FL-Net: A multi-scale cross-decomposition network with frequency external attention for long-term time series forecasting

Many real -world applications, such as energy consumption alerts and long-term traffic planning, require the prediction of data changes over extended horizons. Long-term time series forecasting (LTSF) demands methods with robust prediction capabilities. Recently, transformer -based methods have shown immense potential for LTSF. However, these methods rely heavily on positional encoding to maintain temporal information, inevitably leading to the loss of temporal patterns. Moreover, various self -attention mechanisms often capture only intrasequence features, requiring a greater ability to capture intersequence features. The quadratic complexities of time and memory render training challenging when dealing with lengthy input sequences. We propose FL -Net to enhance the accuracy of LTSF. To capture the seasonal and trend components in the time series accurately, FL -Net segments the input sequences into coarse -grained trends and seasonal components using moving averages. Two sets of encoders extract the temporal features from these components. Our proposed frequency external attention method utilizes two external, compact, learnable, and shared memories to learn and store the time- and frequency -domain features of the entire training set, demonstrating high efficiency in terms of linear complexity. Simultaneously, we propose a multi -scale cross -decomposition method that further decomposes trends and seasonal elements into finer -grained components, thereby enhancing the capability of the model to extract temporal features. Experimental results on nine real -world benchmark datasets demonstrate that FL -Net achieves higher prediction accuracy in long-term forecasting than state-of-the-art methods.