标题： 卷积自编码器、聚类和POD用于纳维-斯托克斯方程的低维参数化 显示英文标题

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

摘要： 大规模动力系统的仿真需要昂贵的计算。 高维状态的低维参数化，如本征正交分解（POD），可以通过在准确性和模型复杂性之间提供一定的权衡来减轻负担。 然而，对于真正低维的参数化（例如控制器设计），像POD这样的线性方法会达到其自然极限，因此非线性方法将成为首选方法。 在本工作中，我们提出了一种由非线性编码器和仿射线性解码器组成的卷积自编码器（CAE），并考虑了与k均值聚类的组合以提高编码性能。 所提出的的方法集在两个由不可压缩纳维-斯托克斯方程建模的圆柱尾流场景中与标准的POD方法进行了比较。 显示英文摘要

摘要： 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.