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

TL;DR

This paper introduces a convolutional autoencoder combined with clustering techniques to achieve low-dimensional nonlinear parametrizations of Navier-Stokes simulations, outperforming traditional linear methods like POD in complex flow scenarios.

Contribution

It proposes a novel nonlinear autoencoder-based approach with clustering for efficient low-dimensional modeling of fluid dynamics.

Findings

Autoencoder-based methods outperform POD in complex flow scenarios.

Clustering improves encoding performance.

The approach reduces computational costs for large-scale simulations.

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.