Kavli Affiliate: Max Tegmark
| First 5 Authors: Ali Ghorashi, Sachin Vaidya, Ziming Liu, Charlotte Loh, Thomas Christensen
| Summary:
Topological photonic crystals (PhCs) offer robust, disorder-resistant modes
engendered by nontrivial band symmetries, but designing PhCs with prescribed
topological band properties remains a challenge due to the complexity involved
in mapping the continuous real-space design landscape of photonic crystals to
the discrete output space of band topology. Here, we introduce a new approach
to address this problem, employing Kolmogorov–Arnold networks (KANs) to
predict and inversely design the band symmetries of two-dimensional PhCs with
two-fold rotational (C2) symmetry. We show that a single-hidden-layer KAN,
trained on a dataset of C2-symmetric unit cells, achieves 99% accuracy in
classifying the symmetry eigenvalues of the lowest transverse-magnetic band.
For interpretability, we use symbolic regression to extract eight algebraic
formulas that characterize the band symmetry classes in terms of the Fourier
components of the dielectric function. These formulas not only retain the full
predictive power of the network but also enable deterministic inverse design.
Applying them, we generate 2,000 photonic crystals with target band symmetries,
achieving over 92% accuracy even for high-contrast, experimentally realizable
structures beyond the training domain.
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