Dimension of an inertial manifold for a chaotic attractor of spatially distributed system is estimated usingautoencoder neural network. The inertial manifold is a low dimensional manifold where the chaotic attractor isembedded. The autoencoder maps system state vectors onto themselves letting them pass through an inner statewith a reduced dimension. The training processes of the autoencoder is shown to depend dramatically on thereduced dimension: a learning curve saturates when the dimension is too small and decays if it is sucient for alossless information transfer. The smallest sucient 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 computeddimension is conrmed by its remarkable coincidence with the one obtained as a number of covariant Lyapunovvectors with vanishing pairwise angles. These vectors are called physical modes. Unlike never having zero anglesresidual ones they are known to span a tangent subspace for the inertial manifold.
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