Quantitative analysis of latent space in airfoil shape generation using variational autoencoders
Quantitative analysis of latent space in airfoil shape generation using variational autoencoders
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DOI：
10.1299/transjsme.21-00212
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
Kazuo Yonekura
中科院分区：
文献类型：
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作者：
Kazuo Yonekura
基于机器学习的翼型生成研究已经得到了广泛的应用，二维层流翼型被视为基准问题。在使用变分自动编码器(VAE)学习翼型形状时，我们知道普通VAE(N-VAE)和超球形VAE(S-VAE)得到的结果有很大的不同。造成这种差异的原因是N-VAE采用标准正态分布作为先验，S-VAE采用VMF分布，但尚未对两者的潜在空间进行定量比较。在这项研究中，我们定量地比较了两种VAE模型的数据嵌入到潜在空间的方式。结果表明，具有不同趋势的数据在N-VAE中相互嵌入较近，而具有相似趋势的数据在S-VAE的潜在空间中相互嵌入较近。这种差异可以用KL发散度和数据特征的差异来解释。在本研究中使用的是NACA翼型数据，数据集不是正态分布的，这在机械设计中通常是其他数据的情况。S-VAE在这种情况下是合适的。
Research on shape generation using machine learning has been widely conducted, and two-dimensional laminar flow airfoils are treated as a benchmark problem. When learning airfoil shapes using variational autoencoders (VAEs), it is known that the results obtained by ordinary VAE (N-VAE) and hyperspherical VAE (S-VAE) differ significantly. The difference is attributed to the fact that the standard normal distribution is used as the prior in N-VAE and the vMF distribution is used in S-VAE, but quantitative comparison of the latent space of both has not been conducted. In this study, we quantitatively compared how the data are embedded in the latent space of both VAE models. It is shown that data with different trends are embedded near each other in N-VAE, while data with similar trends are embedded near each other in the latent space of S-VAE. The difference can be explained by the difference in KL divergence and data characteristics. The NACA airfoil data is used in the present study, and the dataset is not normally distributed, which is usually the case with other data in mechanical design. S-VAE is suitable in such a case.