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

TL;DR

This paper compares deep autoencoders and POD for reduced order modeling of fluid dynamics, demonstrating that autoencoders better capture nonlinear features and improve the efficiency of neural ODE-based dynamic predictions in hydrodynamics applications.

Contribution

It introduces a novel combination of deep autoencoders with neural ODEs for fluid flow model reduction, outperforming traditional POD methods in capturing nonlinear dynamics.

Findings

Deep autoencoders provide more efficient nonlinear manifold learning.

Autoencoders yield a latent space better suited for neural ODE dynamics.

The method performs well on both canonical and real-world hydrodynamics problems.

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 [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.