Convolutional Autoencoders, Clustering and POD for Low-dimensional Parametrization of Navier-Stokes Equations

Abstract

Simulations of large-scale dynamical systems require expensive computations. Low-dimensional parametrization of high-dimensional states such as Proper Orthogonal Decomposition (POD) can be a solution to lessen the burdens by providing a certain compromise between accuracy and model complexity. However, for really low-dimensional parametrizations (for example for controller design) linear methods like the POD come to their natural limits so that nonlinear approaches will be the methods of choice. In this work we propose a convolutional autoencoder (CAE) consisting of a nonlinear encoder and an affine linear decoder and consider combinations with k-means clustering for improved encoding performance. The proposed set of methods is compared to the standard POD approach in two cylinder-wake scenarios modeled by the incompressible Navier-Stokes equations.

arXiv comment16 pages, 12 figures

References in corpus (6)

• PhyGeoNet: Physics-Informed Geometry-Adaptive Convolutional Neural Networks for Solving Parameterized Steady-State PDEs on Irregular Domain
• Low-order model for successive bifurcations of the fluidic pinball
• Reduced order modeling of parametrized systems through autoencoders and SINDy approach: continuation of periodic solutions
• Robust output-feedback stabilization for incompressible flows using low-dimensional ${\mathcal{H}}_{\infty }$-controllers
• Learning finite difference methods for reaction-diffusion type equations with FCNN
• Low-complexity linear parameter-varying approximations of incompressible Navier-Stokes equations for truncated state-dependent Riccati feedback

Cited by in corpus (1)

• Deep polytopic autoencoders for low-dimensional linear parameter-varying approximations and nonlinear feedback design