Attractor Memory for Long-Term Time Series Forecasting: A Chaos Perspective

TL;DR

This paper introduces Attraos, a novel long-term time series forecasting model that leverages chaos theory and attractor invariance to improve prediction accuracy by modeling underlying dynamic systems.

Contribution

It is the first to incorporate chaos theory and attractor invariance into LTSF, using phase space reconstruction and a multi-scale dynamic memory unit for better dynamic structure modeling.

Findings

Attraos outperforms existing LTSF methods on mainstream datasets.

It achieves superior results with only one-twelfth of the parameters.

Theoretical analysis supports the effectiveness of chaos-based modeling.

Abstract

In long-term time series forecasting (LTSF) tasks, an increasing number of models have acknowledged that discrete time series originate from continuous dynamic systems and have attempted to model their dynamical structures. Recognizing the chaotic nature of real-world data, our model, \textbf{\textit{Attraos}}, incorporates chaos theory into LTSF, perceiving real-world time series as observations from unknown high-dimensional chaotic dynamic systems. Under the concept of attractor invariance, Attraos utilizes non-parametric Phase Space Reconstruction embedding and the proposed multi-scale dynamic memory unit to memorize historical dynamics structure and predicts by a frequency-enhanced local evolution strategy. Detailed theoretical analysis and abundant empirical evidence consistently show that Attraos outperforms various LTSF methods on mainstream LTSF datasets and chaotic datasets with only one-twelfth of the parameters compared to PatchTST.