Univariate Conditional Variational Autoencoder for Morphogenic Patterns Design in Frontal Polymerization-Based Manufacturing

Abstract

Under some initial and boundary conditions, the rapid reaction-thermal diffusion process taking place during frontal polymerization (FP) destabilizes the planar mode of front propagation, leading to spatially varying, complex hierarchical patterns in thermoset polymeric materials. Although modern reaction-diffusion models can predict the patterns resulting from unstable FP, the inverse design of patterns, which aims to retrieve process conditions that produce a desired pattern, remains an open challenge due to the non-unique and non-intuitive mapping between process conditions and manufactured patterns. In this work, we propose a probabilistic generative model named univariate conditional variational autoencoder (UcVAE) for the inverse design of hierarchical patterns in FP-based manufacturing. Unlike the cVAE, which encodes both the design space and the design target, the UcVAE encodes only the design space. In the encoder of the UcVAE, the number of training parameters is significantly reduced compared to the cVAE, resulting in a shorter training time while maintaining comparable performance. Given desired pattern images, the trained UcVAE can generate multiple process condition solutions that produce high-fidelity hierarchical patterns.

Figures (8)

• Figure 1: FEM simulation and data generation. (a) problem setup, (b) window of interest, (c) 100 typical pattern examples out of the 4752 total samples.
• Figure 2: Forward model linking the four process conditions to the morphogenic pattern.
• Figure 3: Neural network architecture for inverse design, where the U-Net architecture is the same as the one in the forward model. (a) Conditional variational autoencoder (cVAE) for inverse design, encoding both the design targets (patterns $y$) and the design parameters (process conditions $x$), originally proposed by sohn2015learning. The encoder and decoder have 2,158,711 and 2,166,256 training parameters, respectively. (b) Univariate conditional variational autoencoder (UcVAE) proposed in this work for the inverse pattern design, encoding only the design parameters. The encoder and decoder have 644 and 2,166,256 training parameters, respectively.
• Figure 4: Forward model performance. (a) Normalized root mean squared error (NRMSE) of the test dataset. (b) Comparison between predicted and true patterns of the test dataset, arranged from best (left) to worst (right).
• Figure 5: Model performance of inverse design. Loss values during the training process for cVAE (a) and UcVAE (c). NRMSE between target pattern image from the test dataset and corresponding designed pattern image obtained with cVAE (b) and UcVAE (d). In these figures, one random latent vector $z$ following a standard normal distribution is used to generate one process condition for each sample, and the process conditions are fed into the forward model to obtain the design images.