PAC-LLM Forecasts Chaotic Time Series with LLMs

Forecasting chaotic time series is notoriously difficult due to their extreme sensitivity to initial conditions and inherent long-term unpredictability. Traditional methods typically require extensive historical data to learn the underlying dynamics, making them impractical when only short-term observations are available. While Large Language Models (LLMs) have shown promise in time series forecasting, their temporal representations are not inherently designed for the unique phase-space structure and nonlinear evolution characteristic of chaotic systems. To overcome these limitations, researchers propose PAC-LLM, a phase-space-aware adaptive fusion framework. This framework specifically enables LLMs to forecast long-term chaotic time series by integrating learned phase-space features with textual information. It incorporates an auxiliary feature module and a gated weighting mechanism for effective multivariate coupling information fusion and selection. Extensive experiments conducted on various representative chaotic systems demonstrate that PAC-LLM significantly outperforms existing fine-tuned and zero-shot baselines in both short-term and long-term predictions. An ablation study further confirms the effectiveness of each component within the PAC-LLM framework, highlighting its potential to unlock LLM capabilities for complex, unpredictable forecasting tasks.