Local variations in the 3D microstructure can control the macroscopic behavior of heterogeneous porous materials. For example, the permittivity through porous sheets or membranes is governed by local high‐volume pathways or bottlenecks. Due to local variations, unfeasibly large amounts of microstructure data may be needed to reliably predict such material properties directly from image data. Here it is demonstrated that a vine copula approach provides parametric models for local microstructure descriptors that compactly capture the 3D microstructure including its local variations and efficiently probe it with respect to selected, measurable properties. In contrast to common methods of complexity reduction, the proposed approach creates parametric models for the multivariate probability distribution of high‐dimensional descriptor vectors that inherently contain the complex, nonlinear dependencies between these descriptors. Therein, material properties are offered in physically motivated distributions of microstructure descriptors rather than as normally distributed data. Applied to porous fiber networks (paper) before and after unidirectional compression, it is shown that the copula‐based models reveal material‐characteristic relationships between two or more microstructure descriptors. In this way, the presented modeling approach can provide deeper insight into the microscopic origin of effective macroscopic properties of heterogeneous porous materials.

中文翻译：

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R-Vine Copulas 用于多孔材料中描述符关系的数据驱动量化

3D 微观结构的局部变化可以控制异质多孔材料的宏观行为。例如，通过多孔片或膜的介电常数受局部大容量路径或瓶颈控制。由于局部变化，可能需要大量不可行的微观结构数据来直接从图像数据可靠地预测此类材料特性。这里证明了 vine copula 方法为局部微观结构描述符提供了参数化模型，可以紧凑地捕获 3D 微观结构（包括其局部变化），并根据选定的可测量属性对其进行有效探测。与常见的降低复杂性的方法相比，所提出的方法为高维描述符向量的多元概率分布创建参数模型，这些模型本质上包含这些描述符之间复杂的非线性依赖性。其中，材料特性以微观结构描述符的物理驱动分布形式提供，而不是作为正态分布数据。应用于单向压缩前后的多孔纤维网络（论文）表明，基于联结的模型揭示了两个或多个微观结构描述符之间的材料特性关系。通过这种方式，所提出的建模方法可以更深入地了解异质多孔材料有效宏观性能的微观起源。