Tackling the Nonlinearity Problem in Inverse Modeling: Mixture Density Network-Backed Quantized AutoEncoder

Generative models have been widely used in the field of computer vision due to their ability to produce unseen data points. Its application has proven to be useful in various scientific domains such as materials science for generating new microstructure images that require learning nonlinear and one-to-many property-microstructure relationships. However, existing simulation-based solutions for this application are inefficient and time-consuming. Moreover, nonlinearity from the lower to higher dimensions poses considerable challenges. In this work, we propose a novel Mixture Density Network (MDN) based Quan-tized Autoencoder Network designed to generate microstructure images from only a single data point by establishing one-to-many nonlinear relationships from property to microstructure. Once the autoencoder effectively compresses spatial information into the property domain, we use the combination of produced latent vectors and property values to create a supplementary dataset for MDN. Upon completion of the model training, generative structures are extracted and merged to create a framework that generates images based on target property values (i.e., absorption values in this study). The trained MDN demonstrates proficiency in generating latent vectors within distribution, while the proposed Vector Quantized Variational Autoencoder (VQ-VAE) efficiently maps the embedding table to the latent space, generating images from property values within the range of properties observed during training. We demonstrate that our proposed model consistently outperforms the baselines with respect to generating new microstructure images having target properties and overcoming the above-mentioned challenges.