Machine Learning for predicting chaotic systems

2024-07-29

arXiv.org

AI Summary

Chaotic systems—such as weather—pose fundamental challenges for predictive modeling due to extreme sensitivity to initial conditions, complicating reliable forecasting. Method: We conduct a systematic evaluation of lightweight and heavyweight machine learning models across multiple benchmark datasets, including a newly constructed dataset with quantifiable uncertainty. We propose the Cumulative Maximum Error (CME) as a robust evaluation metric, design a computational-cost-aware hyperparameter optimization strategy, and integrate uncertainty quantification with temporal modeling. Contribution/Results: Experiments demonstrate that carefully tuned simple models often significantly outperform unadapted state-of-the-art deep models. Model complexity must align with intrinsic data characteristics; indiscriminately increasing architectural complexity harms generalization and reliability. Our work establishes “fitness over complexity” as a core principle for chaotic forecasting and provides a reproducible, methodology-driven framework for scientific machine learning.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Stochastic Optimization
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Web Mining and Content Analysis: Machine learning and data science for the Web
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Predicting chaotic dynamical systems is critical in many scientific fields, such as weather forecasting, but challenging due to the characteristic 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 benchmark databases, as well as a newly introduced database that allows for uncertainty quantification in the benchmark results. In addition to state-of-the-art methods from the literature, we also present new advantageous variants of established methods. Hyperparameter tuning is adjusted based on computational cost, with more tuning allocated to less costly methods. Furthermore, we introduce the cumulative maximum error, a novel metric that combines desirable properties of traditional metrics and is 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 highlight the importance of aligning prediction methods with data characteristics and caution against the indiscriminate use of overly complex models.

Problem

• Compare machine learning methods for chaotic system prediction.
• Evaluate performance using benchmark databases and new metrics.
• Highlight importance of method alignment with data characteristics.

Innovation

• Compares lightweight and heavyweight ML architectures
• Introduces new database for uncertainty quantification
• Proposes cumulative maximum error metric