Zero-shot forecasting of chaotic systems (2409.15771v2)

Abstract: Time-series forecasting is a challenging problem that traditionally requires specialized models custom-trained for the specific task at hand. Recently, inspired by the success of LLMs, foundation models pre-trained on vast amounts of time-series data from diverse domains have emerged as a promising candidate for general-purpose time-series forecasting. The defining characteristic of these foundation models is their ability to perform zero-shot learning, that is, forecasting a new system from limited context data without explicit re-training or fine-tuning. Here, we evaluate whether the zero-shot learning paradigm extends to the challenging task of forecasting chaotic systems. Across 135 distinct chaotic dynamical systems and $10^8$ timepoints, we find that foundation models produce competitive forecasts compared to custom-trained models (including NBEATS, TiDE, etc.), particularly when training data is limited. Interestingly, even after point forecasts fail, large foundation models are able to preserve the geometric and statistical properties of the chaotic attractors. We attribute this success to foundation models' ability to perform in-context learning and identify context parroting as a simple mechanism used by these models to capture the long-term behavior of chaotic dynamical systems. Our results highlight the potential of foundation models as a tool for probing nonlinear and complex systems.

• The paper presents a large-scale evaluation of foundation models using 10^8 timepoints across 135 chaotic systems to benchmark prediction quality.
• It shows that models like Chronos preserve the long-term attractor geometry even when point forecasts fail, ensuring dynamic consistency.
• The study demonstrates that scaling model size improves forecasting accuracy and reduces retraining needs, offering practical benefits in real-world applications.

Zero-shot Forecasting of Chaotic Systems

The paper "Zero-shot forecasting of chaotic systems" by Yuanzhao Zhang and William Gilpin presents an empirical evaluation of foundation models' ability to perform zero-shot forecasting of chaotic systems. Utilizing the paradigm shift inspired by LLMs, the authors explore the potential of pre-trained models on vast time-series data for the challenging task of forecasting chaotic systems without explicit re-training.

Key Contributions

1. Large-scale evaluation of foundation models: The authors conducted a comprehensive benchmark involving 135 distinct chaotic dynamical systems and a total of $10^8$ timepoints. Key numerical metrics such as Valid Prediction Time (VPT) and Symmetric Mean Absolute Percentage Error (sMAPE) were used to evaluate the prediction quality of foundation models, particularly the Chronos model, which demonstrated competitive performance compared to specialized models trained on system-specific data.
2. Long-term attractor reconstruction: Even after point forecasts fail, foundation models like Chronos were found to preserve the geometric and statistical properties of chaotic attractors. This suggests an inherent ability of these models to capture the long-term behavior of chaotic systems, which is critical for understanding the system's dynamics in a broader context.
3. Scaling with model size: The empirical results highlight that larger foundation models exhibit improved forecasting performance, indicating that the scale of the model contributes significantly to its generalization abilities. This is consistent with findings in other areas of machine learning, where larger models tend to perform better due to their capacity to capture more complex patterns and relationships.
4. In-context learning and practical benefits: The paper emphasizes the computational benefits of zero-shot forecasting, particularly when training data is limited. The inference costs are manageable, and the performance of models like Chronos scales well with the context length provided for forecasting. This implies that foundation models can be highly practical in real-world applications where retraining for each specific task is impractical or infeasible.

Implications and Future Directions

Practical Implications:

The findings of this research have significant implications for the field of time-series forecasting, particularly in domains requiring the prediction of complex, nonlinear systems like climate modeling, financial markets, and various engineering applications. The ability to provide competitive zero-shot forecasts means that foundation models can serve as robust general-purpose forecasters, reducing the need for specialized model training and thereby saving computational resources and time.

Theoretical Implications:

The success of Chronos in forecasting chaotic systems underscores the potential of applying high-dimensional transformations and probabilistic frameworks to effectively capture dynamics that are traditionally challenging. This opens up new avenues for research into the interplay between machine learning and dynamical systems theory, particularly in understanding the underlying mechanisms enabling such generalization.

Future Developments:

The paper opens several interesting directions for future research. Firstly, fine-tuning foundation models on specific chaotic systems could further enhance their forecasting capabilities. Additionally, extending the capabilities of models like Chronos to handle multivariate time series natively would broaden their application scope. Another promising avenue is to explore the in-context learning capabilities further and understand the limits of extrapolation that these models can achieve in truly novel scenarios.

Computational Considerations:

The paper also sheds light on the computational trade-offs involved. While zero-shot models avoid the heavy cost of training, their inference times need to be optimized, especially when handling longer context windows. Enhancements in attention mechanisms, as seen in newer architectures, could address these inefficiencies and make such models even more practical.

Overall, the paper by Zhang and Gilpin provides a valuable insight into the capabilities and potential of foundation models in zero-shot forecasting of chaotic systems. The findings suggest not only practical applications but also stimulate further research into understanding and improving these models' performance and applicability to a wider range of complex forecasting tasks.