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Proceedings Paper

Estimating of the inertial manifold dimension for a chaotic attractor of complex Ginzburg-Landau equation using a neural network
Author(s): Pavel V. Kuptsov; Anna V. Kuptsova
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Paper Abstract

Dimension of an inertial manifold for a chaotic attractor of spatially distributed system is estimated using autoencoder neural network. The inertial manifold is a low dimensional manifold where the chaotic attractor is embedded. The autoencoder maps system state vectors onto themselves letting them pass through an inner state with a reduced dimension. The training processes of the autoencoder is shown to depend dramatically on the reduced dimension: a learning curve saturates when the dimension is too small and decays if it is sufficient for a lossless information transfer. The smallest sufficient value is considered as a dimension of the inertial manifold, and the autoencoder implements a mapping onto the inertial manifold and back. The correctness of the computed dimension is confirmed by its remarkable coincidence with the one obtained as a number of covariant Lyapunov vectors with vanishing pairwise angles. These vectors are called physical modes. Unlike never having zero angles residual ones they are known to span a tangent subspace for the inertial manifold.

Paper Details

Date Published: 3 June 2019
PDF: 10 pages
Proc. SPIE 11067, Saratov Fall Meeting 2018: Computations and Data Analysis: from Nanoscale Tools to Brain Functions, 110670N (3 June 2019); doi: 10.1117/12.2523235
Show Author Affiliations
Pavel V. Kuptsov, Yuri Gagarin State Technical Univ. of Saratov (Russian Federation)
Anna V. Kuptsova, Yuri Gagarin State Technical Univ. of Saratov (Russian Federation)


Published in SPIE Proceedings Vol. 11067:
Saratov Fall Meeting 2018: Computations and Data Analysis: from Nanoscale Tools to Brain Functions
Dmitry Engelevich Postnov, Editor(s)

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