2018/11/23 by Kuptsov, Pavel V., Kuptsova, Anna V.
#Computational Physics (physics.comp-ph) #FOS: Computer and information sciences #FOS: Physical sciences #Machine Learning (cs.LG)
paper · doi:10.48550/arxiv.1811.11851
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.