Symmetry-aware super-resolution of crystal orientation maps via invariant latent-space learning
Abstract
Crystal-orientation maps are physical fields defined only up to crystal symmetry; electron backscatter diffraction (EBSD) resolves them experimentally, but acquisition-time constraints limit spatial resolution. Unlike conventional images, EBSD data lie on the quotient space SO(3)/G, where G is the crystal-symmetry group. Standard Euclidean interpolation can therefore mix symmetry-equivalent representations and blur grain boundaries. We introduce the Symmetry-Group-Aware Super-Resolution Attention Network (SG-SRAN), which incorporates crystal symmetry and boundary preservation by design. A frozen, locally isometric encoder maps equivalent orientations to a common latent representation in which Euclidean distance approximates misorientation. Super-resolution is performed in this space, with each high-resolution token restricted to a feature-consistent local support to prevent cross-boundary mixing. A dictionary-based decoder then recovers valid orientations. Across FCC and HCP benchmarks, SG-SRAN matches 15-16 million parameter backbones using only 27-49k trainable parameters, while achieving the lowest p68 errors, highest inverse-pole-figure fidelity, and zero-shot transfer to unseen alloys.
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BibTeX
@misc{garg2026symmetryaware,
title = {{Symmetry-aware super-resolution of crystal orientation maps via invariant latent-space learning}},
author = {Umang Garg and Warren Zamudio and McLean P. Echlin and Samantha H. Daly and Tresa M. Pollock and B. S. Manjunath},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10898},
eprint = {2609.10898},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10898},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Symmetry-aware super-resolution of crystal orientation maps via invariant latent-space learning
AU - Umang Garg
AU - Warren Zamudio
AU - McLean P. Echlin
AU - Samantha H. Daly
AU - Tresa M. Pollock
AU - B. S. Manjunath
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.10898
UR - https://arxiv.org/abs/2609.10898
AB - Crystal-orientation maps are physical fields defined only up to crystal symmetry; electron backscatter diffraction (EBSD) resolves them experimentally, but acquisition-time constraints limit spatial resolution. Unlike conventional images, EBSD data lie on the quotient space SO(3)/G, where G is the crystal-symmetry group. Standard Euclidean interpolation can therefore mix symmetry-equivalent representations and blur grain boundaries. We introduce the Symmetry-Group-Aware Super-Resolution Attention Network (SG-SRAN), which incorporates crystal symmetry and boundary preservation by design. A frozen, locally isometric encoder maps equivalent orientations to a common latent representation in which Euclidean distance approximates misorientation. Super-resolution is performed in this space, with each high-resolution token restricted to a feature-consistent local support to prevent cross-boundary mixing. A dictionary-based decoder then recovers valid orientations. Across FCC and HCP benchmarks, SG-SRAN matches 15-16 million parameter backbones using only 27-49k trainable parameters, while achieving the lowest p68 errors, highest inverse-pole-figure fidelity, and zero-shot transfer to unseen alloys.
ER -