Fast descriptor-based 2D and 3D microstructure reconstruction using the Portilla–Simoncelli algorithm

IF 8.7 2区 工程技术 Q1 Mathematics Engineering with Computers Pub Date : 2024-07-22 DOI:10.1007/s00366-024-02026-7
Paul Seibert, Alexander Raßloff, Karl Kalina, Markus Kästner
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Abstract

Reconstructing microstructures from statistical descriptors is a key enabler of computer-based inverse materials design. In the Yeong–Torquato algorithm and other common methods, the problem is approached by formulating it as an optimization problem in the space of possible microstructures. In this case, the error between the desired microstructure and the current reconstruction is measured in terms of a descriptor. As an alternative, descriptors can be regarded as constraints defining subspaces or regions in the microstructure space. Given a set of descriptors, a valid microstructure can be obtained by sequentially projecting onto these subspaces. This is done in the Portilla–Simoncelli algorithm, which is well known in the field of texture synthesis. Noting the algorithm’s potential, the present work aims at introducing it to microstructure reconstruction. After exploring its capabilities and limitations in 2D, a dimensionality expansion is developed for reconstructing 3D volumes from 2D reference data. The resulting method is extremely efficient, as it allows for high-resolution reconstructions on conventional laptops. Various numerical experiments are conducted to demonstrate its versatility and scalability. Finally, the method is validated by comparing homogenized mechanical properties of original and reconstructed 3D microstructures.

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使用波蒂利亚-西蒙切利算法快速重建基于描述符的二维和三维微观结构
根据统计描述符重构微观结构是基于计算机的反向材料设计的关键因素。在 Yeong-Torquato 算法和其他常用方法中,问题是通过在可能的微观结构空间中将其表述为优化问题来解决的。在这种情况下,所需的微观结构与当前重建之间的误差用描述符来衡量。另一种方法是将描述符视为微观结构空间中定义子空间或区域的约束条件。给定一组描述符,按顺序投影到这些子空间,就能得到有效的微观结构。在纹理合成领域广为人知的 Portilla-Simoncelli 算法就是这样实现的。注意到该算法的潜力,本研究旨在将其引入微观结构重建。在探索了该算法在二维领域的能力和局限性后,我们开发了一种维度扩展方法,用于从二维参考数据重建三维体积。由此产生的方法非常高效,因为它可以在传统笔记本电脑上进行高分辨率重建。为了证明该方法的多功能性和可扩展性,我们进行了各种数值实验。最后,通过比较原始三维微结构和重建三维微结构的均质机械性能,验证了该方法的有效性。
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来源期刊
Engineering with Computers
Engineering with Computers 工程技术-工程:机械
CiteScore
16.50
自引率
2.30%
发文量
203
审稿时长
9 months
期刊介绍: Engineering with Computers is an international journal dedicated to simulation-based engineering. It features original papers and comprehensive reviews on technologies supporting simulation-based engineering, along with demonstrations of operational simulation-based engineering systems. The journal covers various technical areas such as adaptive simulation techniques, engineering databases, CAD geometry integration, mesh generation, parallel simulation methods, simulation frameworks, user interface technologies, and visualization techniques. It also encompasses a wide range of application areas where engineering technologies are applied, spanning from automotive industry applications to medical device design.
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