Crystal orientation super-resolution

SG-SRAN

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

The model respects crystal symmetry before it learns spatial reconstruction, then routes high-resolution predictions among locally supported orientation branches.

Read the method View repository

FCC proper cubic group O

HCP proper hexagonal group D6

4x4 reported reconstruction setting

27-49k trainable backbone parameters

Method

Work on orientations, not raw coordinates

A crystal orientation is an equivalence class in SO(3)/G. SG-SRAN encodes that quotient structure explicitly and keeps the learned backbone compact.

Encode

Direct Reynolds projection sends symmetry-equivalent orientations to the same latent representation.

Route

Feature-space clusters define local candidates. The router selects a candidate for each high-resolution subpixel.

Refine and decode

High-resolution convolutions refine the routed field before a fixed dictionary returns unit quaternions.

SG-SRAN pipeline from low-resolution EBSD orientations through invariant encoding, routed upsampling, refinement, and dictionary decoding — End-to-end SG-SRAN pipeline and the local support, proposal, and routing operations inside the upsampler.

Representation

One construction, symmetry-specific harmonic content

The FCC encoder uses one degree-4 even block and produces a 9-dimensional feature. The HCP encoder retains degrees 2, 4, and 6 and produces a 40-dimensional feature.

Fixed block scales calibrate the local latent metric so that small feature distances track small misorientation angles. The encoder-dictionary pair is then checked by round-trip recovery on the experimental orientations.

FCC / O: 1 x 4e, l = {4}
HCP / D6: 1 x 2e + 1 x 4e + 2 x 6e

FCC and HCP invariant encoder fields, local distance response, and symmetry-copy precision — Invariant fields, local metric response, and numerical invariance for FCC and HCP.

Evidence

Evaluation across two crystal systems

The study compares four deterministic interpolants and seven learned baselines over five seeds, with symmetry-aware misorientation, IPF fidelity, and boundary metrics.

0.0076 rad FCC encoder-dictionary round trip

0.0079 rad HCP encoder-dictionary round trip

Zero-shot evaluation on unseen FCC and HCP alloys

IN718 FCC low-resolution input, SG-SRAN reconstruction, high-resolution target, residual, and IPF key — **IN718, FCC.** Low-resolution input, SG-SRAN reconstruction, high-resolution target, and IPF-space residual.

Ti-6Al-4V HCP low-resolution input, SG-SRAN reconstruction, high-resolution target, residual, and IPF key — **Ti-6Al-4V, HCP.** Low-resolution input, SG-SRAN reconstruction, high-resolution target, and IPF-space residual.

Use

Train, infer, and inspect

Reference configurations preserve the reported FCC and HCP encoder, routing, and refinement settings.

Prepare data

Each dataset root contains dataset_info.json and matched quaternion arrays under Train, Val, and Test.

Select symmetry

Start from configs/in718_fcc_4x4.json or configs/ti6al4v_hcp_4x4.json, then set dataset_root.

Check outputs

Inference writes unit-quaternion arrays, IPF maps, and summary metrics under the experiment directory.

Train

python -m training.train_iso_embedding_ocrp \
  --exp_dir experiments/IN718/sgsran_4x4 \
  --config config_new.json \
  --gpu_ids 0

Infer

python -m inference.infer_iso_embedding_sr_attn \
  --exp_dir experiments/IN718/sgsran_4x4 \
  --config config_new.json \
  --checkpoint best_model.pt \
  --split Test \
  --gpu_ids 0

Repository

Implementation and diagnostics

The repository includes the invariant encoders, routed backbone, training and inference entry points, representation diagnostics, and regression tests.

Open SG-SRAN on GitHub