AI-Driven Control of Chaos: A Transformer-Based Approach for Dynamical Systems

TL;DR

This paper introduces a transformer-based machine learning algorithm for controlling chaos in dynamical systems, enabling efficient, real-time confinement of particles without relying on complex physical models.

Contribution

It presents a novel, model-free approach using transformers to accurately compute control bounds for chaotic systems, improving efficiency over traditional methods.

Findings

High accuracy with mean squared error of 2.88e-4

Fast computation times in seconds

Effective real-time control of chaotic systems

Abstract

Chaotic behavior in dynamical systems poses a significant challenge in trajectory control, traditionally relying on computationally intensive physical models. We present a machine learning-based algorithm to compute the minimum control bounds required to confine particles within a region indefinitely, using only samples of orbits that iterate within the region before diverging. This model-free approach achieves high accuracy, with a mean squared error of $2.88 \times 10^{-4}$ and computation times in the range of seconds. The results highlight its efficiency and potential for real-time control of chaotic systems.