Nonlinear proper orthogonal decomposition for convection-dominated flows
- URL: http://arxiv.org/abs/2110.08295v1
- Date: Fri, 15 Oct 2021 18:05:34 GMT
- Title: Nonlinear proper orthogonal decomposition for convection-dominated flows
- Authors: Shady E. Ahmed, Omer San, Adil Rasheed, Traian Iliescu
- Abstract summary: We propose an end-to-end Galerkin-free model combining autoencoders with long short-term memory networks for dynamics.
Our approach not only improves the accuracy, but also significantly reduces the computational cost of training and testing.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Autoencoder techniques find increasingly common use in reduced order modeling
as a means to create a latent space. This reduced order representation offers a
modular data-driven modeling approach for nonlinear dynamical systems when
integrated with a time series predictive model. In this letter, we put forth a
nonlinear proper orthogonal decomposition (POD) framework, which is an
end-to-end Galerkin-free model combining autoencoders with long short-term
memory networks for dynamics. By eliminating the projection error due to the
truncation of Galerkin models, a key enabler of the proposed nonintrusive
approach is the kinematic construction of a nonlinear mapping between the
full-rank expansion of the POD coefficients and the latent space where the
dynamics evolve. We test our framework for model reduction of a
convection-dominated system, which is generally challenging for reduced order
models. Our approach not only improves the accuracy, but also significantly
reduces the computational cost of training and testing.
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