Abstract

Model reduction for fluid flow simulation continues to be of great interest across a number of scientific and engineering fields. In a previous work [1], 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 latentspace that appears to be more suitable for capturing the temporal dynamics through the NODE framework.

Abstract

Various modal decomposition techniques have been developed in the last decade [1­11]. We focus on data-driven approches, and since data flow volume is increasing day by day, it is important to study the performance of order reduction and feature detection algorithms. In this work we compare the performance and feature detection behaviour of energy and frequency based algorithms (Proper Orthogonal Decomposition [1­3] and Dynamic Mode Decomposition [4­6, 8­11]) on two data set testcases taken from fluid dynamics.

Abstract