Deep convolutional neural network for shape optimization using level-set approach
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This article presents a reduced-order modeling methodology for shape optimization applications via deep convolutional neural networks (CNNs). 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, and suited for non-intrusive applications. We demonstrate our complete ROM-based shape optimization on a gradient-based three-dimensional shape optimization problem to minimize the induced drag of a wing in potential flow. We show a satisfactory comparison between ROM-based optima for the aerodynamic coefficients compared to their counterparts obtained via a potential flow solver. The predicted behavior of our ROM-based global optima closely matches the 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 full order model-based online optimization applications. Thus, it promises a tractable solution for shape optimization of complex configuration and physical problems.
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