Machine Learning for predicting chaotic systems

Christof Schötz, Alistair White, Maximilian Gelbrecht, Niklas Boers

Abstract:

Predicting chaotic dynamical systems is critical in many scientific fields such as weather
prediction, but challenging due to the characterising 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, taylored for chaotic
systems. Our results show that well-tuned simple methods, as well as untuned baseline meth-
ods, 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.