Machine Learning for predicting chaotic systems

Predicting chaotic dynamical systems is critical in many scientific fields such as weather prediction, but challenging due to the characterizing sensitive dependence on initial conditions. Traditional modeling approaches require extensive domain knowledge, often leading to a shift towards data-driven methods using machine learning. However, existing research provides inconclusive results on which machine learning methods are best suited for predicting chaotic systems. In this paper, we compare different lightweight and heavyweight machine learning architectures using extensive existing databases, as well as a newly introduced one that allows for uncertainty quantification in the benchmark results. We perform hyperparameter tuning based on computational cost and introduce a novel error metric, the cumulative maximum error, which combines several desirable properties of traditional metrics, tailored for chaotic systems. Our results show that well-tuned simple methods, as well as untuned baseline methods, often outperform state-of-the-art deep learning models, but their performance can vary significantly with different experimental setups. These findings underscore the importance of matching prediction methods to data characteristics and available computational resources.