  We investigate the sensitivity of reduced order models (ROMs) to training
data resolution as well as sampling rate. In particular, we consider proper
orthogonal decomposition (POD), coupled with Galerkin projection (POD-GP), as
an intrusive reduced order modeling technique. For non-intrusive ROMs, we
consider two frameworks. The first is using dynamic mode decomposition (DMD),
and the second is based on artificial neural networks (ANNs). For ANN, we
utilized a residual deep neural network, and for DMD we have studied two
versions of DMD approaches; one with hard thresholding and the other with
sorted bases selection. Also, we highlight the differences between
mean-subtracting the data (i.e., centering) and using the data without
mean-subtraction. We tested these ROMs using a system of 2D shallow water
equations for four different numerical experiments, adopting combinations of
sampling rates and resolutions. For these cases, we found that the DMD basis
obtained with hard threshodling is sensitive to sampling rate, performing worse
at very high rates. The sorted DMD algorithm helps to mitigate this problem and
yields more stabilized and converging solution. Furthermore, we demonstrate
that both DMD approaches with mean subtraction provide significantly more
accurate results than DMD with mean-subtracting the data. On the other hand,
POD is relatively insensitive to sampling rate and yields better representation
of the flow field. Meanwhile, resolution has little effect on both POD and DMD
performances. Therefore, we preferred to train the neural network in POD space,
since it is more stable and better represents our dataset. Numerical results
reveal that an artificial neural network on POD subspace (POD-ANN) performs
remarkably better than POD-GP and DMD in capturing system dynamics, even with a
small number of modes.
