Title: Flames: Multi-Scale Mamba with Adaptive Fourier Filters and Laplace Transform for Time Series Forecasting
Primary area: learning on time series and dynamical systems
Keywords: Time Series Forecasting, Adaptive Fourier Filter, Mamba, Multi- Scale, Laplace Transform

Abstract: Time series data usually exhibit intricate characteristics such as non-stationarity, noise, multi-scale periodicity, and transient dynamics, posing significant challenges to long-term time series forecasting (LTSF). While transformer-based models effectively capture long-range dependencies, their practical applications are hindered by high computational cost with quadratic complexity, noise sensitivity, and overfitting on small datasets. Moreover, time series present distinct patterns at different temporal resolutions, containing both fine-grained (micro) and coarse-grained (macro) information. To address these issues, we propose a novel framework, Flames (multi-scale Fourier Filter Mamba with Laplace), designed for efficient and robust LTSF. Specifically: (i) We introduce an adaptive Fourier filter with a selection module embedded into Mamba. At each scale, the neural operator uses Fourier analysis to refine feature representations, applies learnable thresholds for noise reduction, and captures inter-frequency interactions via global-local semantic filters through element multiplication. (ii) We incorporate the Laplace transform to capture transient dynamics. Extensive experiments on multiple benchmarks demonstrate that Flames consistently outperforms SOTA methods, achieving superior accuracy–efficiency trade-offs. Results highlight its strong robustness and scalability, particularly in noisy or transient settings.