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• W3100846584 abstract "Machine learning models have emerged as powerful tools in physics and engineering. In this work, we use an autoencoder with latent space penalization to discover approximate finite-dimensional manifolds of two canonical partial differential equations. We test this method on the Kuramoto-Sivashinsky (K-S), Korteweg-de Vries (KdV), and damped KdV equations. We show that the resulting optimal latent space of the K-S equation is consistent with the dimension of the inertial manifold. We then uncover a nonlinear basis representing the manifold of the latent space for the K-S equation. The results for the KdV equation show that it is more difficult to recover a reduced latent space, which is consistent with the truly infinite-dimensional dynamics of the KdV equation. In the case of the damped KdV equation, we find that the number of active dimensions decreases with increasing damping coefficient." @default.
• W3100846584 created "2020-11-23" @default.
• W3100846584 creator A5011315981 @default.
• W3100846584 creator A5073916939 @default.
• W3100846584 date "2021-09-03" @default.
• W3100846584 modified "2023-09-25" @default.
• W3100846584 title "Learning a reduced basis of dynamical systems using an autoencoder" @default.
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• W3100846584 doi "https://doi.org/10.1103/physreve.104.034202" @default.
• W3100846584 hasPubMedId "https://pubmed.ncbi.nlm.nih.gov/34654102" @default.
• W3100846584 hasPublicationYear "2021" @default.
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