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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