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

arXiv: https://arxiv.org/abs/2608.29579 · HTML: https://mlsanity.com/paper/2608.29579/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 46 references that are in the map.
- First posted on arXiv 30 Aug 2026.

## Builds on (most cited first, 17 of 17)

- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Qwen2.5-Coder Technical Report](https://mlsanity.com/paper/2409.12186/) (2024)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [N-BEATS: Neural basis expansion analysis for interpretable time series forecasting](https://mlsanity.com/paper/1905.10437/) (2019)
- [Next Generation Reservoir Computing](https://mlsanity.com/paper/2106.07688/) (2021)
- [Data-Driven Forecasting of High-Dimensional Chaotic Systems with Long Short-Term Memory Networks](https://mlsanity.com/paper/1802.07486/) (2018)
- [TimeCMA: Towards LLM-Empowered Multivariate Time Series Forecasting via Cross-Modality Alignment](https://mlsanity.com/paper/2406.01638/) (2024)
- [Chaos as an interpretable benchmark for forecasting and data-driven modelling](https://mlsanity.com/paper/2110.05266/) (2021)
- [Domain Adaptation for Time Series Forecasting via Attention Sharing](https://mlsanity.com/paper/2102.06828/) (2021)
- [LSTPrompt: Large Language Models as Zero-Shot Time Series Forecasters by Long-Short-Term Prompting](https://mlsanity.com/paper/2402.16132/) (2024)
- [LLMs learn governing principles of dynamical systems, revealing an in-context neural scaling law](https://mlsanity.com/paper/2402.00795/) (2024)
- [Zero-shot forecasting of chaotic systems](https://mlsanity.com/paper/2409.15771/) (2024)
- [True Zero-Shot Inference of Dynamical Systems Preserving Long-Term Statistics](https://mlsanity.com/paper/2505.13192/) (2025)
- [Cross-Domain Pre-training with Language Models for Transferable Time Series Representations](https://mlsanity.com/paper/2403.12372/) (2024)
- [LLM-Mixer: Multiscale Mixing in LLMs for Time Series Forecasting](https://mlsanity.com/paper/2410.11674/) (2024)
- [LLM-PS: Empowering Large Language Models for Time Series Forecasting with Temporal Patterns and Semantics](https://mlsanity.com/paper/2503.09656/) (2025)
- [Learning Global and Local Features of Power Load Series Through Transformer and 2D-CNN: An Image-based Multi-step Forecasting Approach Incorporating Phase Space Reconstruction](https://mlsanity.com/paper/2407.11553/) (2024)

## Abstract (arXiv)

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.