论文标题
数据驱动的增强模型减少了计算流体动力学中分叉模型的模型
Data-Driven Enhanced Model Reduction for Bifurcating Models in Computational Fluid Dynamics
论文作者
论文摘要
我们研究了各种数据驱动的方法，以增强基于投影的模型还原技术，目的是捕获分叉溶液。为了显示数据驱动的增强功能的有效性，我们专注于不可压缩的Navier-Stokes方程和不同类型的分叉。为了使解决方案通过HOPF分叉，我们提出了一种将正交分解与Hankel动态模式分解相结合的方法。为了近似接近干草叉分叉的解决方案，我们将局部还原模型与人工神经网络相结合。显示了几个数值示例，以证明所提出的方法的可行性。
We investigate various data-driven methods to enhance projection-based model reduction techniques with the aim of capturing bifurcating solutions. To show the effectiveness of the data-driven enhancements, we focus on the incompressible Navier-Stokes equations and different types of bifurcations. To recover solutions past a Hopf bifurcation, we propose an approach that combines proper orthogonal decomposition with Hankel dynamic mode decomposition. To approximate solutions close to a pitchfork bifurcation, we combine localized reduced models with artificial neural networks. Several numerical examples are shown to demonstrate the feasibility of the presented approaches.
