Many real-world objects are designed by smooth curves, especially in the domain of aerospace and ship, where aerodynamic shapes (e.g., airfoils) and hydrodynamic shapes (e.g., hulls) are designed. To facilitate the design process of those objects, we propose a deep learning based generative model that can synthesize smooth curves. The model maps a low-dimensional latent representation to a sequence of discrete points sampled from a rational B 'ezier curve. We demonstrate the performance of our method in completing both synthetic and real-world generative tasks. Results show that our method can generate diverse and realistic curves, while preserving consistent shape variation in the latent space, which is favorable for latent space design optimization or design space exploration.
As for many curve synthesis problems, our goal is not just to generate curves, but also to facilitate design optimization and design space exploration by using a low-dimensional latent space to represent the geometrical design space. The noise input @math can be regarded as a latent representation of the design space. However, @math from the standard GAN is usually uninterpretable, meaning that the relation between @math and the geometry of generated designs may be disordered and entangled. To mitigate this problem, the InfoGAN @cite_23 uses a set of @math as an extra input to the generator, and regularizes @math by maximizing a lower bound of the mutual information between @math and the generated data. The mutual information lower bound @math is where @math is the entropy of the latent codes, and @math is the auxiliary distribution for approximating @math . We direct interested readers to @cite_23 for the derivation of @math . The InfoGAN objective combines @math with the standard GAN objective: where @math is a weight parameter.
@cite_23
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This paper describes InfoGAN, an information-theoretic extension to the Generative Adversarial Network that is able to learn disentangled representations in a completely unsupervised manner. InfoGAN is a generative adversarial network that also maximizes the mutual information between a small subset of the latent variables and the observation. We derive a lower bound to the mutual information objective that can be optimized efficiently, and show that our training procedure can be interpreted as a variation of the Wake-Sleep algorithm. Specifically, InfoGAN successfully disentangles writing styles from digit shapes on the MNIST dataset, pose from lighting of 3D rendered images, and background digits from the central digit on the SVHN dataset. It also discovers visual concepts that include hair styles, presence absence of eyeglasses, and emotions on the CelebA face dataset. Experiments show that InfoGAN learns interpretable representations that are competitive with representations learned by existing fully supervised methods.