  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.
