  Reduced order modelling relies on representing complex dynamical systems
using simplified modes, which can be achieved through Koopman operator
analysis. However, computing Koopman eigen pairs for high-dimensional
observable data can be inefficient. This paper proposes using deep
autoencoders, a type of deep learning technique, to perform non-linear
geometric transformations on raw data before computing Koopman eigen vectors.
The encoded data produced by the deep autoencoder is diffeomorphic to a
manifold of the dynamical system, and has a significantly lower dimension than
the raw data. To handle high-dimensional time series data, Takens's time delay
embedding is presented as a pre-processing technique. The paper concludes by
presenting examples of these techniques in action.
