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.
3 More- Received 20 October 2020
- Revised 28 April 2021
- Accepted 19 July 2021
DOI:https://doi.org/10.1103/PhysRevE.104.034202
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