Towards Data-Driven Model Reduction of the Navier-Stokes Equations using the Loewner Framework
Towards Data-Driven Model Reduction of the Navier-Stokes Equations using the Loewner Framework
复制标题
使用 Loewner 框架实现纳维-斯托克斯方程的数据驱动模型简化
DOI：
10.1007/978-3-030-90727-3_14
复制
发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Heinkenschloss, Matthias
中科院分区：
文献类型：
--
作者：
Diaz, Alejandro N.;Heinkenschloss, Matthias
将Loewner框架扩展到计算不可压Navier-Stokes方程控制系统的降阶模型。对于二次常微分方程（ODE），它直接从系统的输入输出映射的扩展导出的传递函数分量的测量值构造ROM。给定的测量，没有显式访问系统是必需的，以构建ROM。为了扩展Loewner框架，NS方程转化为常微分方程投影到子空间定义的不可压缩性条件。这种投影在理论上是可以使用的，但在计算上是可以避免的。本文介绍了总体方法。目前，传递函数测量是通过计算模拟获得的;从实验中获得它们是一个悬而未决的问题。数值结果显示了潜在的Loewner框架，但也揭示了可能缺乏的ROM的稳定性。一种可能的方法，目前需要访问NS系统，来处理这些不稳定性的概述。
The Loewner framework is extended to compute reduced order models (ROMs) for systems governed by the incompressible Navier-Stokes (NS) equations. For quadratic ordinary differential equations (ODEs) it constructs a ROM directly from measurements of transfer function components derived from an expansion of the system’s input-to-output map. Given measurements, no explicit access to the system is required to construct the ROM.To extend the Loewner framework, the NS equations are transformed into ODEs by projecting onto the subspace defined by the incompressibility condition. This projection is used theoretically, but avoided computationally. This paper presents the overall approach. Currently, transfer function measurements are obtained via computational simulations; obtaining them from experiments is an open issue. Numerical results show the potential of the Loewner framework, but also reveal possible lack of stability of the ROM. A possible approach, which currently requires access to the NS system, to deal with these instabilities is outlined.