# Machine Learning for Predicting Chaotic Systems

arXiv: https://arxiv.org/abs/2407.20158 · HTML: https://mlsanity.com/paper/2407.20158/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 37 references that are in the map.
- First posted on arXiv 29 Jul 2024.

## Builds on (most cited first, 11 of 11)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [N-BEATS: Neural basis expansion analysis for interpretable time series forecasting](https://mlsanity.com/paper/1905.10437/) (2019)
- [Transformers in Time Series: A Survey](https://mlsanity.com/paper/2202.07125/) (2022)
- [Next Generation Reservoir Computing](https://mlsanity.com/paper/2106.07688/) (2021)
- [Backpropagation Algorithms and Reservoir Computing in Recurrent Neural Networks for the Forecasting of Complex Spatiotemporal Dynamics](https://mlsanity.com/paper/1910.05266/) (2019)
- [Chaos as an interpretable benchmark for forecasting and data-driven modelling](https://mlsanity.com/paper/2110.05266/) (2021)
- [Hybrid Forecasting of Chaotic Processes: Using Machine Learning in Conjunction with a Knowledge-Based Model](https://mlsanity.com/paper/1803.04779/) (2018)
- [Learning unknown ODE models with Gaussian processes](https://mlsanity.com/paper/1803.04303/) (2018)
- [Model scale versus domain knowledge in statistical forecasting of chaotic systems](https://mlsanity.com/paper/2303.08011/) (2023)

## Built on by (most cited first, 4 of 4)

- [Zero-shot forecasting of chaotic systems](https://mlsanity.com/paper/2409.15771/) (2024)
- [Projected Neural Differential Equations for Learning Constrained Dynamics](https://mlsanity.com/paper/2410.23667/) (2024)
- [Minimal Deterministic Echo State Networks Outperform Random Reservoirs in Learning Chaotic Dynamics](https://mlsanity.com/paper/2507.06050/) (2025)
- [Machine-Precision Prediction of Low-Dimensional Chaotic Systems from Noise-Free Data](https://mlsanity.com/paper/2507.09652/) (2025)

## Abstract (arXiv)

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.