Predicting the Unpredictable: LLM-powered Long-term Chaotic Time Series Forecasting under Short-term Observations
Machine Learning
Summary
The authors address the difficulty of predicting chaotic time series, which change unpredictably over time and are hard to forecast with limited data. They create PAC-LLM, a new method that helps Large Language Models better understand chaotic data by using special features related to the system's phase-space and combining multiple information sources carefully. Their experiments show that PAC-LLM predicts chaotic systems more accurately than current methods, both for short-term and long-term forecasts. They also test different parts of their approach to show that each contributes to better performance.
Authors
Yuhang Yao, Bohan Jiang
Abstract
Chaotic time series forecasting is a challenging task due to its sensitivity to initial conditions and long-term unpredictability. Traditional methods typically rely on sufficient temporal trajectories to learn long-term dynamics, which limits their applicability when only short-term observations are available. While recent Large Language Models (LLMs) have shown great potential for time series forecasting, their temporal representations are not explicitly tailored to the phase-space structure and nonlinear evolution of chaotic systems. To address these issues, we propose PAC-LLM, a phase-space-aware adaptive fusion framework for long-term chaotic time series forecasting powered by LLMs. PAC-LLM leverages learned phase-space features and textual information to fully enable LLM's time series forecasting capacity. In particular, we design an auxiliary feature module and a gated weighting mechanism for multivariate coupling information fusion and selection. Extensive experiments on representative chaotic systems demonstrate that our method outperforms existing fine-tuned and zero-shot baselines in both short-term and long-term predictions. Our ablation study further confirms the effectiveness of each key component in PAC-LLM.