We compare two flexible regression methods for predictors that live on SO(3) subgroups corresponding to orientations of grains within metals.
Polycrystalline materials fail under shock-loading when stresses build up and nucleate voids. Quantitative understanding of these processes is needed to assure reliable performance of materials in extreme environments. I will describe collaborative work that seeks to extract phenomenological patterns in simulated micro-scale stress-strain fields. Our eventual goal is to build continuum-scale simulations with porosity effects that are physically well-grounded.
I will describe and apply two flexible regression methods to predict stress fields in an assembly of simulated Tantalum grains. Orientations of crystal lattices are used as predictors in these models and present special challenges because the point group structure of crystal orientations imposes symmetries on the regression problem. One model regresses on (hyper)-spherical harmonic bases. The other is a Gaussian process fit utilizing a distance metric in orientation space. The two methods yield similar predictions with very different computational structure.
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