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.

翻译：异质多孔材料在各类工程系统中发挥着关键作用。微结构表征与重建为这些材料的建模提供了有效手段，这对于开展物理性质模拟、结构-性能关联研究以及提升其在不同应用中的性能至关重要。为实现小样本条件下优越的可控性与适用性，我们提出了一种统计可控的微结构重建框架，该框架将神经网络与切片Wasserstein度量相结合。具体而言，我们的方法利用局部模式分布进行微结构表征，并采用可控采样策略生成满足给定条件参数的目标分布。基于神经网络的模型建立了从输入分布到目标局部模式分布的映射，从而实现微结构重建。切片Wasserstein度量与梯度优化技术的结合最小化了这些分布之间的距离，从而获得稳定可靠的模型。我们的方法即使在小样本条件下也能执行随机且可控的重建任务。此外，通过分块策略，该方法能够生成大尺寸（如512和1024）的三维微结构。通过引入空间位置掩码，我们的方法在生成空间异质且复杂的微结构方面表现优异。我们在多种材料上进行了随机重建、可控重建、异质重建以及大尺寸微结构重建的实验。通过可视化、统计度量及物理性质模拟的对比分析验证了该方法的有效性，为结构-性能关联及材料逆向设计研究提供了新的见解与可能性。