Nonlinear proper orthogonal decomposition for convection-dominated flows

TL;DR

This paper introduces a nonlinear POD framework combining autoencoders and LSTM networks to improve reduced order modeling of convection-dominated flows, reducing error and computational cost.

Contribution

It presents a Galerkin-free, end-to-end nonlinear POD method that constructs a nonlinear mapping for better model reduction of challenging convection-dominated systems.

Findings

Enhanced accuracy over traditional methods

Significant reduction in training and testing computational costs

Effective modeling of convection-dominated flows

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.