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：大规模动态系统的仿真需要高昂的计算成本。对高维状态进行低维参数化（如本征正交分解，POD）能够通过平衡精度与模型复杂度来减轻计算负担。然而，在实现极低维参数化（例如控制器设计场景）时，线性方法（如POD）会达到其固有极限，因此非线性方法将成为优选。本文提出了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），并结合k-means聚类以提升编码性能。将所提出的方法集与标准POD方法在不可压缩纳维-斯托克斯方程建模的两个圆柱尾流场景中进行对比分析。