Neural electron backscatter diffraction
At the mesoscale, the state of a material is described by continuous fields. In polycrystals, crystallographic orientation and defect content vary continuously within grains, and grain boundaries trace continuous curves. Like other spatially resolved characterization methods, electron backscatter diffraction (EBSD) records this continuum on a discrete grid. Every subsequent analysis inherits the grid, whether it is classical Hough indexing or pattern-based machine learning. We introduce neural EBSD, which treats a scan as a continuous and differentiable field of Kikuchi diffraction intensity over specimen and detector coordinates. Two formulations are explored: a joint network over all four coordinates, and a factorized representation that combines continuous specimen-domain coefficient fields with learned detector-domain basis patterns. The factorized formulation exhibits higher accuracy: for recrystallized and additively manufactured Ni-base superalloys, it reconstructs 900,000 Kikuchi patterns per map with mean errors below 1% of the maximum intensity, while reducing data storage nearly 750-fold relative to the raw patterns. Since the learned field is continuous, patterns can be queried at any specimen position. Trained only on a quarter of the scan points, the model recovers withheld patterns whose indexed orientations fall within 4 deg. of reference at 97% of positions in the recrystallized alloy. Analytical spatial derivatives of the differentiable representation provide a diffraction gradient that localizes grain boundaries continuously, free of indexing, disorientation thresholds, and staircase artifacts. The gradient field also exposes intragranular heterogeneity, including dislocation-cell substructure in the as-built alloy.