Autoencoder

Physics

Nonlinear system

Mathematics

Politics

Truncation error

Truncation (statistics)

Algorithm

Machine learning

Political science

Artificial intelligence

Galerkin method

Representation (politics)

Computer science

Quantum mechanics

Applied mathematics

Artificial neural network

Projection (relational algebra)

Physics of Fluids

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.

Nonlinear proper orthogonal decomposition for convection-dominated flows