Neural Ordinary Differential Equations for Data-Driven Reduced Order Modeling of Environmental Hydrodynamics

TL;DR

This paper investigates Neural Ordinary Differential Equations for reduced order modeling of fluid dynamics, demonstrating their stability and accuracy in predicting complex flow systems, with a focus on improving training efficiency for broader applicability.

Contribution

It introduces Neural ODEs as a novel approach for data-driven reduced order modeling of environmental hydrodynamics, comparing their performance with classical methods.

Findings

Neural ODEs offer stable and accurate latent-space dynamics evolution.

They show potential for extrapolatory predictions in fluid flow modeling.

Training time remains a challenge for large-scale system applications.

Abstract

Model reduction for fluid flow simulation continues to be of great interest across a number of scientific and engineering fields. Here, we explore the use of Neural Ordinary Differential Equations, a recently introduced family of continuous-depth, differentiable networks (Chen et al 2018), as a way to propagate latent-space dynamics in reduced order models. We compare their behavior with two classical non-intrusive methods based on proper orthogonal decomposition 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 real-world applications of shallow water hydrodynamics in riverine and estuarine systems. Our findings indicate that Neural ODEs provide an elegant framework for stable and accurate evolution of latent-space dynamics with a promising potential of extrapolatory predictions. However, in order to facilitate their widespread adoption for large-scale systems, significant effort needs to be directed at accelerating their training times. This will enable a more comprehensive exploration of the hyperparameter space for building generalizable Neural ODE approximations over a wide range of system dynamics.