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arXiv · 2410.18003

Inferring stability properties of chaotic systems on autoencoders' latent spaces

Elise Özalp·Luca Magri
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Abstract

The data-driven learning of solutions of partial differential equations can be based on a divide-and-conquer strategy. First, the high dimensional data is compressed to a latent space with an autoencoder; and, second, the temporal dynamics are inferred on the latent space with a form of recurrent neural network. In chaotic systems and turbulence, convolutional autoencoders and echo state networks (CAE-ESN) successfully forecast the dynamics, but little is known about whether the stability properties can also be inferred. We show that the CAE-ESN model infers the invariant stability properties and the geometry of the tangent space in the low-dimensional manifold (i.e. the latent space) through Lyapunov exponents and covariant Lyapunov vectors. This work opens up new opportunities for inferring the stability of high-dimensional chaotic systems in latent spaces.

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Elise Özalp, Luca Magri. 2024-10-23. Inferring stability properties of chaotic systems on autoencoders' latent spaces. https://arxiv.org/abs/2410.18003

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