Inferring stability properties of chaotic systems on autoencoders' latent spaces
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2024
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| _version_ | 1866912083492208640 |
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| author | Özalp, Elise Magri, Luca |
| author_facet | Özalp, Elise Magri, Luca |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_18003 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Inferring stability properties of chaotic systems on autoencoders' latent spaces Özalp, Elise Magri, Luca Machine Learning Chaotic Dynamics 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. |
| title | Inferring stability properties of chaotic systems on autoencoders' latent spaces |
| topic | Machine Learning Chaotic Dynamics |
| url | https://arxiv.org/abs/2410.18003 |