| Autor: |
Sondak D; Institute for Applied Computational Science, Harvard University, Cambridge, Massachusetts 02138, USA., Protopapas P; Institute for Applied Computational Science, Harvard University, Cambridge, Massachusetts 02138, USA. |
| Jazyk: |
angličtina |
| Zdroj: |
Physical review. E [Phys Rev E] 2021 Sep; Vol. 104 (3-1), pp. 034202. |
| DOI: |
10.1103/PhysRevE.104.034202 |
| Abstrakt: |
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. |
| Databáze: |
MEDLINE |
| Externí odkaz: |
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