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.

翻译：预测混沌动力系统在天气预报等诸多科学领域至关重要，但由于其对初始条件的敏感依赖性而极具挑战性。传统建模方法需要深厚的领域知识，这促使研究逐渐转向采用机器学习的数据驱动方法。然而，现有研究对于何种机器学习方法最适合预测混沌系统尚未给出明确结论。本文利用大量现有数据库以及一个新引入的、可在基准结果中进行不确定性量化的数据库，比较了不同的轻量级与重量级机器学习架构。我们基于计算成本进行超参数调优，并引入一种新颖的误差度量——累积最大误差，该度量综合了传统指标的若干理想特性，专为混沌系统定制。研究结果表明，经过良好调优的简单方法以及未经调优的基线方法，其性能常常优于最先进的深度学习模型，但它们的表现可能因实验设置的不同而存在显著差异。这些发现强调了根据数据特征和可用计算资源选择合适的预测方法的重要性。