Data-driven reduced order modeling of environmental hydrodynamics using deep autoencoders and neural ODEs
This work addresses model reduction for environmental hydrodynamics, offering incremental improvements in efficiency and dynamics capture for scientific and engineering applications.
The authors tackled model reduction for fluid flow simulation by using deep autoencoders to discover reduced basis representations, with dynamics approximated by Neural ODEs, and found that this approach achieved highly efficient compression and better suitability for capturing temporal dynamics compared to traditional methods like POD.
Model reduction for fluid flow simulation continues to be of great interest across a number of scientific and engineering fields. In a previous work [arXiv:2104.13962], we explored the use of Neural Ordinary Differential Equations (NODE) as a non-intrusive method for propagating the latent-space dynamics in reduced order models. Here, we investigate employing deep autoencoders for discovering the reduced basis representation, the dynamics of which are then approximated by NODE. The ability of deep autoencoders to represent the latent-space is compared to the traditional proper orthogonal decomposition (POD) approach, again in conjunction with NODE for capturing the dynamics. Additionally, we compare their behavior with two classical non-intrusive methods based on POD and radial basis function interpolation as well as dynamic mode decomposition. The test problems we consider include incompressible flow around a cylinder as well as a real-world application of shallow water hydrodynamics in an estuarine system. Our findings indicate that deep autoencoders can leverage nonlinear manifold learning to achieve a highly efficient compression of spatial information and define a latent-space that appears to be more suitable for capturing the temporal dynamics through the NODE framework.