Tree-based learning for high-fidelity prediction of chaos

Forecasting chaotic systems using machine learning has become highly sought after due to its potential applications in predicting climate and weather phenomena, stock market indices, and pathological activity in biomedical signals. However, existing solutions, such as neural network-based reservoir computing (RC) and long-short-term memory (LSTM), contain numerous model hyperparameters that must be tuned, often requiring high computational resources and large training datasets. Here, we propose a computationally simpler regression tree ensemble-based technique to predict the temporal evolution of chaotic systems in data-driven environments. Furthermore, we introduce a heuristic procedure to prescribe hyperparameters through automated statistical analysis of training data, which eliminates the need for the user to perform hyperparameter tuning. We investigate the efficacy of the proposed hyperparameter prescription procedure through numerical experiments. Lastly, we demonstrate the state-of-the-art performance of our proposed approach on several benchmark tasks, including the Southern Oscillation Index, a crucial but noisy climate time series with limited samples, to illustrate its effectiveness in real-world settings.