Polytopic Autoencoders for Very Low‐Dimensional Parametrizations of Fluid Flow Models

ABSTRACT Model order reduction techniques have been developed to decrease the computational complexity of large‐scale dynamical systems while maintaining a certain level of accuracy. A common approach involves utilizing linear model reduction methods to construct reduced‐order models with a reduced set of degrees of freedom, enabling faster simulations and control design. However, while it projects states and latent variables into linear spaces that are unbounded, in standard linear reduced‐order models, they are typically observed to be bounded. This discrepancy suggests that state reconstruction within a polytope is likely to offer advantages. In this study, we propose a polytopic autoencoder architecture incorporating clustering techniques to realize state reconstruction within a polytope. Furthermore, we demonstrate that this approach achieves satisfactory reconstruction errors compared to a classical linear model reduction method, proper orthogonal decomposition, in simulations of fluid flows.