Inverse design and deep learning for phononic crystals

Abstract

In this talk, I will present some results pertaining to the inverse design of phononic crystals. First, I will consider the design of 3-D phononic crystals exhibiting large omnidirectional bandgaps within the context of topology optimization using the SIMP method. The problem will be presented in the traditional forward-inverse paradigm where the forward solver is a mixed-variational scheme implemented on multiple graphical processing units. The inverse solver is a large scale adjoint based optimization framework with highly efficient vectorized operations for sensitivity calculations. In the second part of the talk, I will consider a deep learning based surrogate model for the forward problem. The neural network architecture is based on convolutional neural networks (CNN) and is trained to predict the phononic eigenvalues of unseen unit cell configurations. I show that a CNN based model easily outperforms traditional neural network architectures such as the multi layer perceptron (MLP) on both efficiency of learning and generalization capabilities. Strong and highly efficient surrogate models such as CNN coupled with topology optimization provide a an important way forward for the inverse design of phononic crystals and metamaterials.