  Reduced Order Modelling (ROM) has been widely used to create lower order,
computationally inexpensive representations of higher-order dynamical systems.
Using these representations, ROMs can efficiently model flow fields while using
significantly lesser parameters. Conventional ROMs accomplish this by linearly
projecting higher-order manifolds to lower-dimensional space using
dimensionality reduction techniques such as Proper Orthogonal Decomposition
(POD). In this work, we develop a novel deep learning framework DL-ROM (Deep
Learning - Reduced Order Modelling) to create a neural network capable of
non-linear projections to reduced order states. We then use the learned reduced
state to efficiently predict future time steps of the simulation using 3D
Autoencoder and 3D U-Net based architectures. Our model DL-ROM is able to
create highly accurate reconstructions from the learned ROM and is thus able to
efficiently predict future time steps by temporally traversing in the learned
reduced state. All of this is achieved without ground truth supervision or
needing to iteratively solve the expensive Navier-Stokes(NS) equations thereby
resulting in massive computational savings. To test the effectiveness and
performance of our approach, we evaluate our implementation on five different
Computational Fluid Dynamics (CFD) datasets using reconstruction performance
and computational runtime metrics. DL-ROM can reduce the computational runtimes
of iterative solvers by nearly two orders of magnitude while maintaining an
acceptable error threshold.
