A Generative Model for Accelerated Inverse Modelling Using a Novel Embedding for Continuous Variables

TL;DR

The paper addresses the challenge of conditioning generative models on continuous material properties for rapid microstructure design. It introduces a binary floating-point embedding based on IEEE 754 representation, forming the BcGAN, to preserve precision and enable fine-grained control, and contrasts it with binning and autoencoder-based approaches (CcGAN, CGAN variants). Results on Ising-model data show that CcGAN suffers mode collapse and poor property capture, while BcGAN accurately reproduces temperature-conditioned microstructures across the full range and near the Curie temperature, with a robust latent space and efficient training. The work demonstrates that careful embedding design enables exact structure–property control and suggests a path toward accelerated, data-driven materials design.

Abstract

In materials science, the challenge of rapid prototyping materials with desired properties often involves extensive experimentation to find suitable microstructures. Additionally, finding microstructures for given properties is typically an ill-posed problem where multiple solutions may exist. Using generative machine learning models can be a viable solution which also reduces the computational cost. This comes with new challenges because, e.g., a continuous property variable as conditioning input to the model is required. We investigate the shortcomings of an existing method and compare this to a novel embedding strategy for generative models that is based on the binary representation of floating point numbers. This eliminates the need for normalization, preserves information, and creates a versatile embedding space for conditioning the generative model. This technique can be applied to condition a network on any number, to provide fine control over generated microstructure images, thereby contributing to accelerated materials design.

Figures (11)

• Figure 1: Binary representation example of a float32 number. Here, the number $0.42$ is shown in binary representation, with its three components clearly separated.
• Figure 2: From left to right: 3D representation of the model response and visualization of the interpolated model response. From the slope and intercept of the generated images, we can map them to the corresponding temperature-property.
• Figure 3: Comparison of the two PSD parameters and the microstructures for both embedding strategies. Each temperature is sampled 100 times to get an average estimation of the model response.
• Figure 4: Comparison of the two PSD parameters and the microstructures for the CGAN with different numbers of classes. Each temperature is sampled 100 times to get an average estimation of the model response. Here, we can clearly see that increasing the number of classes gives increasingly worse results.
• Figure 5: Output activity of the first 10 neurons from the embedding space of each generator model. For the CGAN architecture, the first 10 entries of the lookup table are used for the classes case.