Predicting the Unpredictable: LLM-powered Long-term Chaotic Time Series Forecasting under Short-term Observations

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.