Design of Phononic Bandgap Metamaterials Based on Gaussian Mixture Beta Variational Autoencoder and Iterative Model Updating

Abstract

Phononic bandgap metamaterials, which consist of periodic cellular structures, are capable of absorbing energy within a certain frequency range. Designing metamaterials that trap waves across a wide wave frequency range is still a challenging task. In this paper, we present a deep feature learning-based design framework for both unsupervised generative design and supervised learning-based exploitative optimization. The Gaussian mixture beta variational autoencoder (GM-βVAE) is employed to extract latent features as design variables. Gaussian Process (GP) regression models are trained to predict the relationship between latent features and the properties for the property-driven optimization. The optimal structural designs are reconstructed by mapping the optimized latent feature values to the original image space. Compared with the regular variational autoencoder (VAE), we demonstrate that GM-βVAE has better learning capability and is able to generate a more diversified design set in unsupervised generative design. Furthermore, we propose an iterative GM-βVAE model updating-based design framework. In each iteration, the optimal designs found property-driven optimization are used to update the training dataset. The GM-βVAE model is re-trained with the updated dataset for the optimization search in the next iteration. A comparative study between the traditional single-loop and the iterative approaches is presented to demonstrate the effectiveness of the iterative framework. The caveats to designing phonic bandgap metamaterials are summarized.

Deep-learning-based inverse design of three-dimensional architected cellular materials with the target porosity and stiffness using voxelized Voronoi lattices

“…The neural network architecture yields two main outputs that are necessary for the inverse design of mechanical metamaterials: the modeling parameters, which can be used to generate geometries with additional modeling processes [ 41–43 ], and the geometries in the form of pixels or voxels [ 11 , 46 , 47 , 59 , 60 ]. The straightforward generation of geometries can speed up the inverse design process and directly visualize geometries.…”

“…The straightforward generation of geometries can speed up the inverse design process and directly visualize geometries. The variational autoencoder (VAE) and GANs are the most commonly used neural network architectures for straightforward generation [ 47 , 59 , 60 ]. In the VAE, an encoder learns to represent input data (e.g.…”

Data‐Driven Design for Metamaterials and Multiscale Systems: A Review

“…While the training of most neural network‐based models normally requires large datasets, GP was employed when there was a relatively small amount of training data. [ 87,213 ] GP's ability to estimate uncertainty makes it well‐suited for adaptive sampling and Bayesian optimization. These are useful design techniques especially when the computation of responses is time‐consuming.…”

“…Wang et al. [ 213 ] used a Gaussian mixture beta variational autoencoder (GM‐βVAE) to reduce the dimension of the pixelated metamaterials design representation. Chen et al.…”

“…To obtain the metamaterial design solution, a common approach is to use the property prediction model as a surrogate design evaluation model and incorporate it into any iterative optimization loop. [ 40,45,159,208,209,212,213 ] Besides iterative optimization, past works also employed virtual screening [ 221 ] and sampling [ 37,102,210 ] to select design solutions, which also took advantage of the fast design evaluation capability of property prediction models.…”