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

TL;DR

FLDmamba is a novel framework that combines Fourier and Laplace transforms with Mamba to improve long-term time series prediction by capturing multi-scale periodicity and transient dynamics more effectively.

Contribution

The paper introduces FLDmamba, integrating Fourier and Laplace transforms with Mamba, to enhance time series prediction accuracy and robustness against noise, addressing limitations of existing models.

Findings

Outperforms Transformer-based models on benchmarks.

Effectively captures multi-scale periodicity and transient dynamics.

Demonstrates robustness to data noise.

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 cannot capture multi-scale periodicity and transient dynamics effectively. Meanwhile, they are susceptible to data noise issues 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. Our extensive experiments demonstrate that FLDmamba achieves superior performance on time series prediction benchmarks, outperforming both Transformer-based and other Mamba-based architectures. To promote the reproducibility of our method, we have made both the code and data accessible via the following URL:{\href{https://github.com/AI4Science-WestlakeU/FLDmamba}{https://github.com/AI4Science-WestlakeU/\model}.