  Multiple shapes must be obtained in the mechanical design process to satisfy
the required design specifications. The inverse design problem has been
analyzed in previous studies to obtain such shapes. However, finding multiple
shapes in a short computation period is difficult while using the conventional
methods. This paper proposes the use of the conditional variational
autoencoders (CVAE) with normal distribution, denoted by N-CVAE, along with the
von Mises-Fischer distribution, denoted by S-CVAE, to find multiple solutions
for the inverse design problems. Both the CVAE models embed shapes into a
latent space. The S-CVAE enables the separation of data in the latent space,
whereas the N-CVAE embeds the data in a narrow space. These different features
are used for various tasks in this study. In one of the tasks, the dataset
consists of only one type of data and generates similar airfoils. Here, S-CVAE
outperforms N-CVAE because it can separate the data. Another task involves
combining different types of airfoils and generating new types of data. N-CVAE
is useful in this instance since it embeds different shapes in the same latent
area, due to which, the model outputs intermediate shapes of different types.
The shape-generation capability of S-CVAE and N-CVAE are experimentally
compared in this study.
