In recent years, there has been growing interest in the use of machine learning for numerical simulations in physics. This master’s thesis examines how machine learning, specifically Recurrent Neural Networks (RNNs), can contribute to the analysis and simulation of dynamical systems. The thesis is divided into two main parts: the first part explores the use of RNNs for trajectory classification based on their chaotic behavior, while the second part investigates how RNNs can serve as a substitute for traditional mathematical models of dynamical systems.
In the first part, we focus on the classification of trajectories of the standard map, one of the fundamental models for studying chaos. The parameter K, which appears in the standard map, determines the degree of chaos in the trajectories. We explore different approaches to training RNNs, training the models both on fixed values of K and over broader intervals, to assess their capability to generalize.
The second part of the thesis is dedicated to modeling the standard map using RNNs as autoregressive models. We investigate the ability of RNNs to replicate system dynamics and provide both short-term and long-term predictions. The emphasis is placed on the potential use of RNNs to accelerate computations in cases where traditional numerical methods are computationally expensive.
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