FLDmamba: Integrating Fourier and Laplace Transform Decomposition with Mamba for Enhanced Time Series Prediction

Qianru Zhang, Chenglei Yu, Haixin Wang, Yudong Yan, Yuansheng Cao, Hongzhi Yin, Siu Ming Yiu, Tailin Wu

Keywords: Mamba; Time Series Prediction

Abstract: Time series prediction, a crucial task across various domains, faces significant challenges due to the inherent complexities of time series data, including non-stationarity, multi-scale periodicity, and transient dynamics, particularly when tackling long-term predictions. While Transformer-based architectures have shown promise, their quadratic complexity with sequence length hinders their efficiency for long-term predictions. Recent advancements in State-Space Models, such as Mamba, offer a more efficient alternative for long-term modeling, but they lack the capability to capture multi-scale periodicity and transient dynamics effectively. Meanwhile, they are susceptible to the data noise issue in time series. This paper proposes a novel framework, FLDmamba (Fourier and Laplace Transform Decomposition Mamba), addressing these limitations. FLDmamba leverages the strengths of both Fourier and Laplace transforms to effectively capture both multi-scale periodicity, transient dynamics within time series data, and improve the robustness of the model to the data noise issue. By integrating Fourier analysis into Mamba, FLDmamba enhances its ability to capture global-scale properties, such as multi-scale periodicity patterns, in the frequency domain. Meanwhile, the Fourier Transform aids in isolating underlying patterns or trends from noise in time series data by emphasizing key frequency components, thereby enabling the model to mitigate noise effects. Additionally, incorporating Laplace analysis into Mamba improves its capacity to capture local correlations between neighboring data points, leading to a more accurate representation of transient dynamics. Our extensive experiments demonstrate that FLDmamba achieves superior performance on time series prediction benchmarks, outperforming both Transformer-based and other Mamba-based architectures. This work offers a computationally efficient and effective solution for long-term time series prediction, paving the way for its application in real-world scenarios. To promote the reproducibility of our method, we have made both the code and data accessible via the following URL: \href{https://anonymous.4open.science/r/FLambas-AD7E/README.md}{https://anonymous.4open.science/r/FLDmamba}

Primary Area: other topics in machine learning (i.e., none of the above)

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Submission Number: 4022