We introduce the Voronoi fundamental zone octonion interpolation framework for grain boundary (GB) structure-property models and surrogates. The VFZO framework offers an advantage over other five degree-of-freedom based property interpolation methods because it is constructed as a point set in a manifold. This means that directly computed Euclidean distances approximate the original octonion distance with significantly reduced computation runtime (~7 CPU minutes vs. 153 CPU days for a 50000x50000 pairwise-distance matrix). This increased efficiency facilitates lower interpolation error through the use of significantly more input data. We demonstrate grain boundary energy interpolation results for a non-smooth validation function and simulated bi-crystal datasets for Fe and Ni using four interpolation methods: barycentric interpolation, Gaussian process regression (GPR), inverse-distance weighting, and nearest-neighbor interpolation. These are evaluated for 50000 random input GBs and 10 000 random prediction GBs. The best performance was achieved with GPR, which resulted in a reduction of the root mean square error (RMSE) by 83.0% relative to RMSE of a constant, average model. Likewise, interpolation on a large, noisy, molecular statics Fe simulation dataset improves performance by 34.4% compared to 21.2% in prior work. Interpolation on a small, low-noise MS Ni simulation dataset is similar to interpolation results for the original octonion metric (57.6% vs. 56.4%). A vectorized, parallelized, MATLAB interpolation function (interp5DOF.m) and related routines are available in our VFZO repository (github.com/sgbaird-5dof/interp) which can be applied to other crystallographic point groups. The VFZO framework offers advantages for computing distances between GBs, estimating property values for arbitrary GBs, and modeling surrogates of computationally expensive 5DOF functions and simulations.

中文翻译：

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通过Voronoi基本区八进制框架对任意晶粒边界进行五自由度属性插值

我们介绍了用于晶界（GB）结构属性模型和代理的Voronoi基本区八重音插值框架。VFZO框架相对于其他五种基于自由度的属性插值方法具有优势，因为它被构造为流形中的一个点集。这意味着直接计算的欧几里得距离近似于原始八角距离，同时大大减少了计算时间（对于50000x50000配对距离矩阵，大约为7 CPU分钟，而153 CPU天）。通过使用大量输入数据，提高的效率有助于降低插值误差。我们使用四种插值方法展示了非光滑验证函数的晶界能量插值结果以及Fe和Ni的模拟双晶数据集：重心插值，高斯过程回归（GPR），反距离加权和最近邻插值。对它们进行了50000个随机输入GB和10000个随机预测GB的评估。GPR可获得最佳性能，相对于恒定平均模型的RMSE，均方根误差（RMSE）降低了83.0％。同样，在较大的，嘈杂的分子静力学Fe模拟数据集上进行插值可将性能提高34.4％，而先前的工作则为21.2％。在小的，低噪声的MS Ni模拟数据集上的插值与原始八度度量的插值结果相似（57.6％对56.4％）。向量化，并行化的MATLAB插值函数（interp5DOF.m）和相关例程可在我们的VFZO存储库（github。com / sgbaird-5dof / interp），可以应用于其他晶体学点组。VFZO框架提供了以下优势：计算GB之间的距离，估计任意GB的属性值以及对计算上昂贵的5DOF函数和模拟的替代进行建模。