In this paper, the authors address the challenge of finding mathematical models to describe the behavior of chaotic dynamical systems. They propose a framework that uses neural networks to learn the dynamics of a system and identify missing model terms from observational data. This information is then used by a symbolic regression algorithm to extract explicit mathematical expressions. The framework is tested on various complex chaotic systems, including the Lorenz system, and is shown to accurately recover the known analytical expressions. This approach has the potential to advance our understanding of chaotic systems and enable predictions of future behavior.
https://arxiv.org/abs/2312.14237