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Model reduction for fluid flow simulation continues to be of great interestacross a number of scientific and engineering fields. In a previous work[arXiv:2104.13962], we explored the use of Neural Ordinary DifferentialEquations (NODE) as a non-intrusive method for propagating the latent-spacedynamics in reduced order models. Here, we investigate employing deepautoencoders for discovering the reduced basis representation, the dynamics ofwhich are then approximated by NODE. The ability of deep autoencoders torepresent the latent-space is compared to the traditional proper orthogonaldecomposition (POD) approach, again in conjunction with NODE for capturing thedynamics. Additionally, we compare their behavior with two classicalnon-intrusive methods based on POD and radial basis function interpolation aswell as dynamic mode decomposition. The test problems we consider includeincompressible flow around a cylinder as well as a real-world application ofshallow water hydrodynamics in an estuarine system. Our findings indicate thatdeep autoencoders can leverage nonlinear manifold learning to achieve a highlyefficient compression of spatial information and define a latent-space thatappears to be more suitable for capturing the temporal dynamics through theNODE framework.

Data-driven reduced order modeling of environmental hydrodynamics using deep autoencoders and neural ODEs