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

2025-07-17

AI Summary

Long-term time series forecasting faces challenges including non-stationarity, difficulty in modeling multi-scale periodicity and transient dynamics, low computational efficiency, and poor robustness to noise. To address these, we propose FLDmamba—a novel framework that integrates a Fourier-Laplace decomposition mechanism into the state-space model Mamba for the first time. Specifically, a Fourier branch explicitly captures multi-scale periodic patterns, while a Laplace branch models transient dynamics and decay characteristics; their synergy enhances frequency-domain representation capability and noise robustness. This design overcomes Mamba’s limitations in periodic pattern learning and transient response, while avoiding Transformer’s quadratic computational complexity. Extensive experiments on multiple standard benchmarks demonstrate that FLDmamba significantly outperforms Transformers and state-of-the-art Mamba variants in both prediction accuracy and generalization. Code and data are publicly available.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data
• Natural Language Processing: Learning & Optimization for NLP

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization

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}.

Problem

• Addresses long-term time series prediction challenges
• Improves multi-scale periodicity and transient dynamics capture
• Enhances robustness to data noise in time series

Innovation

• Combines Fourier and Laplace transforms with Mamba
• Captures multi-scale periodicity and transient dynamics
• Enhances robustness to data noise in time series