The parity gap in crystal tensor prediction
Crystal symmetry dictates whether a physical response tensor must vanish, establishing a direct test for machine learning predictions independent of property calculations. We derive the parity gap, a group-theoretic metric quantifying the piezoelectric tensor freedom permitted by a crystal's proper rotation subgroup $SO(3)$ but eliminated by inversion symmetry in $O(3)$. Across state-of-the-art equivariant neural network architectures, unconstrained $SO(3)$ models systematically predict forbidden non-zero responses matching the parity gap of each centrosymmetric crystal class, while polar distortion paths dynamically map output responses to the loss of inversion symmetry. Regression contr...
| Authors | Can Polat, Mustafa Kurban, Erchin Serpedin et al. |
|---|---|
| Primary category | cond-mat.mtrl-sci |
| Published | 19 August 2026 |
| Last updated at source | 16 September 2026 |
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