  Projection-based model order reduction on nonlinear manifolds has been
recently proposed for problems with slowly decaying Kolmogorov n-width such as
advection-dominated ones. These methods often use neural networks for manifold
learning and showcase improved accuracy over traditional linear
subspace-reduced order models. A disadvantage of the previously proposed
methods is the potential high computational costs of training the networks on
high-fidelity solution snapshots. In this work, we propose and analyze a novel
method that overcomes this disadvantage by training a neural network only on
subsampled versions of the high-fidelity solution snapshots. This method
coupled with collocation-based hyper-reduction and Gappy-POD allows for
efficient and accurate surrogate models. We demonstrate the validity of our
approach on a 2d Burgers problem.
