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Dimension of an inertial manifold for a chaotic attractor of spatiallydistributed system is estimated using autoencoder neural network. The inertialmanifold is a low dimensional manifold where the chaotic attractor is embedded.The autoencoder maps system state vectors onto themselves letting them passthrough an inner state with a reduced dimension. The training processes of theautoencoder is shown to depend dramatically on the reduced dimension: alearning curve saturates when the dimension is too small and decays if it issufficient for a lossless information transfer. The smallest sufficient valueis considered as a dimension of the inertial manifold, and the autoencoderimplements a mapping onto the inertial manifold and back. The correctness ofthe computed dimension is confirmed by its remarkable coincidence with the oneobtained as a number of covariant Lyapunov vectors with vanishing pairwiseangles. These vectors are called physical modes. Unlike never having zeroangles residual ones they are known to span a tangent subspace for the inertialmanifold.

Estimating of the inertial manifold dimension for a chaotic attractor of complex Ginzburg-Landau equation using a neural network