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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 usingsignificantly lesser parameters. Conventional ROMs accomplish this by linearlyprojecting higher-order manifolds to lower-dimensional space usingdimensionality reduction techniques such as Proper Orthogonal Decomposition(POD). In this work, we develop a novel deep learning framework DL-ROM (DeepLearning - Reduced Order Modelling) to create a neural network capable ofnon-linear projections to reduced order states. We then use the learned reducedstate to efficiently predict future time steps of the simulation using 3DAutoencoder and 3D U-Net based architectures. Our model DL-ROM is able tocreate highly accurate reconstructions from the learned ROM and is thus able toefficiently predict future time steps by temporally traversing in the learnedreduced state. All of this is achieved without ground truth supervision orneeding to iteratively solve the expensive Navier-Stokes(NS) equations therebyresulting in massive computational savings. To test the effectiveness andperformance of our approach, we evaluate our implementation on five differentComputational Fluid Dynamics (CFD) datasets using reconstruction performanceand computational runtime metrics. DL-ROM can reduce the computational runtimesof iterative solvers by nearly two orders of magnitude while maintaining anacceptable error threshold.

Deep Learning for Reduced Order Modelling and Efficient Temporal Evolution of Fluid Simulations