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

• URL: http://arxiv.org/abs/2104.13962v1
• Date: Thu, 22 Apr 2021 19:20:47 GMT
• Title: Neural Ordinary Differential Equations for Data-Driven Reduced Order Modeling of Environmental Hydrodynamics
• Authors: Sourav Dutta, Peter Rivera-Casillas, Matthew W. Farthing
• Abstract summary: We explore the use of Neural Ordinary Differential Equations for fluid flow simulation. Test problems we consider include incompressible flow around a cylinder and 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.
• Score: 4.547988283172179
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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