  This article presents a reduced-order modeling methodology via deep
convolutional neural networks (CNNs) for shape optimization applications. The
CNN provides a nonlinear mapping between the shapes and their associated
attributes while conserving the equivariance of these attributes to the shape
translations. To implicitly represent complex shapes via a CNN-applicable
Cartesian structured grid, a level-set method is employed. The CNN-based
reduced-order model (ROM) is constructed in a completely data-driven manner
thus well suited for non-intrusive applications. We demonstrate our ROM-based
shape optimization framework on a gradient-based three-dimensional shape
optimization problem to minimize the induced drag of a wing in low-fidelity
potential flow. We show a good agreement between ROM-based optimal aerodynamic
coefficients and their counterparts obtained via a potential flow solver. The
predicted behavior of the optimized shape is consistent with theoretical
predictions. We also present the learning mechanism of the deep CNN model in a
physically interpretable manner. The CNN-ROM-based shape optimization algorithm
exhibits significant computational efficiency compared to the full-order
model-based online optimization applications. The proposed algorithm promises
to develop a tractable DL-ROM-driven framework for shape optimization and
adaptive morphing structures.
