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arXiv · 2501.17588

Controlling Transient Chaos in the Lorenz System with Machine Learning

David Valle·Rubén Capeans·Alexandre Wagemakers·Miguel A. F. Sanjuán
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Abstract

This paper presents a novel approach to sustain transient chaos in the Lorenz system through the estimation of safety functions using a transformer-based model. Unlike classical methods that rely on iterative computations, the proposed model directly predicts safety functions without requiring fine-tuning or extensive system knowledge. The results demonstrate that this approach effectively maintains chaotic trajectories within the desired phase space region, even in the presence of noise, making it a viable alternative to traditional methods. A detailed comparison of safety functions, safe sets, and their control performance highlights the strengths and trade-offs of the two approaches.

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David Valle, Rubén Capeans, Alexandre Wagemakers, Miguel A. F. Sanjuán. 2025-01-29. Controlling Transient Chaos in the Lorenz System with Machine Learning. https://doi.org/10.1140/epjs%2Fs11734-025-01589-w

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