基于卷积神经网络的流体动力学非线性模态分解
Nonlinear mode decomposition with convolutional neural networks for fluid dynamics
摘要：
提出了一种新的非线性模式分解方法，称为模式分解卷积神经网络自动编码器（MD-CNN-AE）。将所提出的方法应用于$Re_D=100$的圆柱绕流作为测试用例。将流属性映射为潜在空间中的两种模式，然后将这两种模式在物理空间中可视化。由于具有非线性激活函数的MD-CNN-AE显示出比适当正交分解（POD）更低的重建误差，因此激活函数中包含的非线性被认为是提高模型性能的关键。通过将POD应用于使用具有双曲正切激活的MD-CNN-AE分解的每个场，发现单个非线性MD-CNN-AE模式包含多个正交基，与线性方法相反，即，POD和具有线性激活的MD-CNN-AE。我们进一步评估拟议的MD-CNN-AE通过将其应用于圆柱体尾流的瞬态过程，以检查其对包含高阶空间模式的流的能力。目前的研究结果表明，一个很大的潜力的非线性MD-CNN-AE被用于流场的特征提取在较低的维度比POD，同时保留与传统的POD模式的可解释的关系。
英文摘要：
We present a new nonlinear mode decomposition method to visualize the decomposed flow fields, named the mode decomposing convolutional neural network autoencoder (MD-CNN-AE). The proposed method is applied to a flow around a circular cylinder at $Re_D=100$ as a test case. The flow attributes are mapped into two modes in the latent space and then these two modes are visualized in the physical space. Because the MD-CNN-AEs with nonlinear activation functions show lower reconstruction errors than the proper orthogonal decomposition (POD), the nonlinearity contained in the activation function is considered the key to improve the capability of the model. It is found by applying POD to each field decomposed using the MD-CNN-AE with hyperbolic tangent activation that a single nonlinear MD-CNN-AE mode contains multiple orthogonal bases, in contrast to the linear methods, i.e., POD and the MD-CNN-AE with linear activation. We further assess the proposed MD-CNN-AE by applying it to a transient process of a circular cylinder wake in order to examine its capability for flows containing high-order spatial modes. The present results suggest a great potential for the nonlinear MD-CNN-AE to be used for feature extraction of flow fields in lower dimension than POD, while retaining interpretable relationships with the conventional POD modes.
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