Inverse design of microstructures using conditional continuous normalizing flows

Inverse design is a classical mathematical challenge found in various fields, including materials science, where it is essential for property-driven microstructure design. This problem involves the inversion of structure-property linkages, a task complicated by the high dimensionality and stochastic nature of microstructures. Leveraging the advantages of a low-dimensional and meaningful design representation, we aim to develop an efficient data-driven approach for the inverse design of microstructures. Specifically, we propose PoreFlow, a modular framework utilizing continuous normalizing flows (CNFs) for property-based microstructure generation. Our approach regularizes the CNF latent space by introducing target properties as a feature vector. Demonstrating the conditional generation process in our framework, we highlight its capabilities as an end-to-end, high-throughput solution for materials inverse design applications. Through an example of generating 3D images of porous microstructures, we analyze the mechanism through which specified targets effectively guide the generative process in low-dimensional latent space. The model's performance in reconstructing and generating new samples with targeted properties was assessed using visual comparison and statistical measures such as RMSE and ² R ² scores. During reconstruction, we consistently achieved ² R ² scores above 91.5 for all five target properties, while for generation, ² R ² scores remained consistently higher than 0.92. Notably, our methodology avoids common issues such as unstable training and mode collapse, which often plague generative models such as GANs, even with extensive hyperparameter tuning. This framework offers a robust solution for advancing inverse microstructure design.