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.

翻译：大规模动力系统仿真需要高昂的计算成本。针对高维状态的低维参数化方法（如本征正交分解POD）可通过在精度与模型复杂度间达成特定权衡来减轻计算负担。然而在极低维参数化（如控制器设计）场景中，POD等线性方法会达到其固有极限，此时非线性方法将成为优选方案。本文提出一种由非线性编码器与仿射线性解码器构成的卷积自编码器（CAE），并考虑结合k-means聚类以提升编码性能。我们将所提方法集与标准POD方法在不可压缩Navier-Stokes方程建模的两个圆柱尾流场景中进行对比。