Nonlinear proper orthogonal decomposition for convection-dominated flows
Nonlinear proper orthogonal decomposition for convection-dominated flows
复制标题
DOI：
10.1063/5.0074310
复制
发表时间：
2021-12-01
影响因子：
4.6
通讯作者：
Iliescu, Traian
中科院分区：
文献类型：
--
作者：
Ahmed, Shady E.;San, Omer;Iliescu, Traian
自编码器技术越来越普遍地用于降阶建模，作为创建潜在空间的一种手段。当与时间序列预测模型集成时，这种降阶表示为非线性动力系统提供了模块化数据驱动建模方法。在这篇论文中，我们提出了一个非线性固有正交分解（POD）框架，它是一个端到端的无galerkin模型，结合了自编码器和长短期记忆网络的动态。通过消除Galerkin模型截断导致的投影误差，该方法的关键是在POD系数的全秩展开和动力学演化的潜在空间之间建立非线性映射的运动学构造。我们测试了我们的框架，用于对流主导系统的模型约简，这通常是对降阶模型的挑战。我们的方法不仅提高了准确率，而且显著降低了训练和测试的计算成本。由AIP出版社独家授权出版。
Autoencoder techniques find increasingly common use in reduced order modeling as a means to create a latent space. This reduced order representation offers a modular data-driven modeling approach for nonlinear dynamical systems when integrated with a time series predictive model. In this Letter, we put forth a nonlinear proper orthogonal decomposition (POD) framework, which is an end-to-end Galerkin-free model combining autoencoders with long short-term memory networks for dynamics. By eliminating the projection error due to the truncation of Galerkin models, a key enabler of the proposed nonintrusive approach is the kinematic construction of a nonlinear mapping between the full-rank expansion of the POD coefficients and the latent space where the dynamics evolve. We test our framework for model reduction of a convection-dominated system, which is generally challenging for reduced order models. Our approach not only improves the accuracy, but also significantly reduces the computational cost of training and testing. Published under an exclusive license by AIP Publishing.