Symmetry-aware super-resolution of crystal orientation maps via invariant latent-space learning

• URL: http://arxiv.org/abs/2609.10898v1
• Date: Wed, 09 Sep 2026 23:03:05 GMT
• Title: Symmetry-aware super-resolution of crystal orientation maps via invariant latent-space learning
• Abstract summary: We introduce the Symmetry-Group-Aware Super-Resolution Attention Network (SG-SRAN), which incorporates crystal symmetry and boundary preservation by design.<n>Super-resolution is performed in this space, with each high-resolution token restricted to a feature-consistent local support to prevent cross-boundary mixing.<n>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.
• Score: 4.722566018999561
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $\mathrm{SO}(3)/G$, 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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