Deep convolutional neural network for shape optimization using level-set approach. (arXiv:2201.06210v2 [math.OC] UPDATED)

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 …

arxiv convolutional neural network math network neural network optimization