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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