Convolutional Autoencoders, Clustering and POD for Low-dimensional Parametrization of Navier-Stokes Equations
This addresses the need for efficient nonlinear parametrization in fluid dynamics simulations, though it is incremental as it builds on existing autoencoder and clustering methods.
The paper tackled the problem of low-dimensional parametrization for large-scale Navier-Stokes simulations by proposing a convolutional autoencoder combined with k-means clustering, achieving improved performance over standard Proper Orthogonal Decomposition in cylinder-wake scenarios.
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.