  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.
