Neural Network Powered Adjoint Methods - Gradient Based Shape Optimization with Deep Learning

Recent work has shown that Neural Networks, especially Convolutional Neural Networks (CNNs), can serve as powerful surrogate models for physical processes regarding input shapes. However, two major issues stand in the way of deep learning based shape optimization using prediction from these surrogate models: how to represent shape functions to feed to the networks, and how to efficiently and accurately compute gradients of the predicted output quantity of interest with respect to the input shape coordinates for optimization. In this work, we present a pipeline for efficient shape optimization that includes an optimal shape representation based on simplex-mesh Fourier transforms, training a CNN-based surrogate model for the prediction of physical quantitates, and a method for backpropagating gradients into original shape coordinates. We illustrate the effectiveness of the methodology with a case study for 2D airfoil optimization.