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

TL;DR

This work tackles the challenge of controllable microstructure reconstruction for heterogeneous porous materials from small samples. It introduces a neural-network framework that maps Gaussian inputs to local pattern distributions and uses a sliced-Wasserstein distance to align reconstructed distributions with a controllable target derived from conditional parameters, enabling 2D-to-3D reconstruction, spatial heterogeneity, and large-size generation via chunking. The key innovations are the local pattern distribution descriptor within a Markov Random Field framework, a principled control strategy for defining target distributions, and a lightweight CNN architecture that supports efficient training and inference. The approach is validated across multiple materials and properties, demonstrating accurate structure replication, controllable statistics, and faithful physical-property predictions, with practical implications for structure–property studies and inverse material design.

Abstract

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.

Figures (22)

• Figure 1: The whole system workflow for structure–property linkage study, including (1) microscopic imaging and pre-processing, (2) microstructure characterization and reconstruction, (3) performance evaluation, and (4) conditional generation and linkage study.
• Figure 2: The framework of statistically controllable microstructure reconstruction.
• Figure 3: Visual comparisons among reference images, target microstructures and partial reconstruction results. Microstructures M1–M4 are silica material, porous rock, battery electrode material, and superalloy, respectively.
• Figure 4: Comparisons of statistical correlation functions. (a) and (b) 2-point probability function curves between the reconstruction results and the target structure for silica material and porous rock; (c) and (d) 2-point probability function curves between the reconstruction results and the reference image for battery electrode material and superalloy. The subfigure is a zoom-in of the starting point region with annotations for the starting point value, phase volume fraction.
• Figure 5: Thermal conductivity analysis of the target structure and the reconstruction results for silica material. (a) temperature field of the target structure, (b)–(e) temperature field of some reconstruction samples, and (f) comparison of thermal conductivity parameters of the target structure and the reconstruction samples.