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arXiv 2403.03571cond-mat.mtrl-scimath.OC
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用于多晶建模的各向异性幂图:通过最优输运高效生成弯曲晶粒

Anisotropic power diagrams for polycrystal modelling: efficient generation of curved grains via optimal transport

Maciej Buze, Jean Feydy, Steven M. Roper, Karo Sedighiani, David P. Bourne

AI总结:

针对各向异性幂图(APDs)生成计算成本高的问题,提出依托GPU适配的快速最优输运算法生成指定统计特性的APDs的方法,可快速生成高分辨率微观结构,还配套开源Python库PyAPD。

摘要:

金属和泡沫的微观结构可通过各向异性幂图(anisotropic power diagrams,简称APDs)有效建模,该方法可控制单个晶粒的形状。APDs更广泛应用的一大主要障碍是其生成相关的计算成本。我们提出了一种生成具有指定统计特性的APDs的新方法,包括对单个晶粒尺寸的精细控制。为此,我们依托可在图形处理器(Graphics Processing Unit,简称GPU)上良好流式运行的快速最优输运算法,这些算法可处理非均匀的各向异性距离函数。这使我们能够找到最贴合实验数据的大型APDs,并在(数十)秒内生成合成高分辨率微观结构。这为其在计算均匀化中的应用解锁了可能,这对需要生成大量代表性微观结构集合作为训练数据的机器学习方法尤为重要。本文配套了一个Python库PyAPD,可在以下网址免费获取:www.github.com/mbuze/PyAPD。

英文摘要:

The microstructure of metals and foams can be effectively modelled with anisotropic power diagrams (APDs), which provide control over the shape of individual grains. One major obstacle to the wider adoption of APDs is the computational cost that is associated with their generation. We propose a novel approach to generate APDs with prescribed statistical properties, including fine control over the size of individual grains. To this end, we rely on fast optimal transport algorithms that stream well on Graphics Processing Units (GPU) and handle non-uniform, anisotropic distance functions. This allows us to find large APDs that best fit experimental data and generate synthetic high-resolution microstructures in (tens of) seconds. This unlocks their use for computational homogenisation, which is especially relevant to machine learning methods that require the generation of large collections of representative microstructures as training data. The paper is accompanied by a Python library, PyAPD, which is freely available at: www.github.com/mbuze/PyAPD.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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