Statistically controllable microstructure reconstruction framework for heterogeneous materials using sliced-Wasserstein metric and neural networks

Heterogeneous porous materials play a crucial role in various engineering systems. Microstructure characterization and reconstruction provide effective means for modeling these materials, which are critical for conducting physical property simulations, structure-property linkage studies, and enhancing their performance across different applications. To achieve superior controllability and applicability with small sample sizes, we propose a statistically controllable microstructure reconstruction framework that integrates neural networks with sliced-Wasserstein metric. Specifically, our approach leverages local pattern distribution for microstructure characterization and employs a controlled sampling strategy to generate target distributions that satisfy given conditional parameters. A neural network-based model establishes the mapping from the input distribution to the target local pattern distribution, enabling microstructure reconstruction. Combinations of sliced-Wasserstein metric and gradient optimization techniques minimize the distance between these distributions, leading to a stable and reliable model. Our method can perform stochastic and controllable reconstruction tasks even with small sample sizes. Additionally, it can generate large-size (e.g. 512 and 1024) 3D microstructures using a chunking strategy. By introducing spatial location masks, our method excels at generating spatially heterogeneous and complex microstructures. We conducted experiments on stochastic reconstruction, controllable reconstruction, heterogeneous reconstruction, and large-size microstructure reconstruction across various materials. Comparative analysis through visualization, statistical measures, and physical property simulations demonstrates the effectiveness, providing new insights and possibilities for research on structure-property linkage and material inverse design.