Nonlinear proper orthogonal decomposition for convection-dominated flows
This work addresses a domain-specific problem in computational fluid dynamics for researchers and engineers dealing with convection-dominated systems, offering an incremental improvement over existing reduced order modeling techniques.
The authors tackled the challenge of model reduction for convection-dominated flows, which are difficult for reduced order models, by proposing a nonlinear proper orthogonal decomposition framework that combines autoencoders with long short-term memory networks. Their approach improved accuracy and significantly reduced computational costs in training and testing.
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.