KANs with learnable univariate spline activations on edges achieve better accuracy than MLPs with fewer parameters, faster scaling, and direct visualization for scientific discovery.
Strong localization of photons in certain disordered dielectric superlattices
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Kolmogorov n-widths of band structure solution manifolds decay exponentially with the minimum spectral gap, establishing sharp optimality bounds for linear reduced-order models.
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KAN: Kolmogorov-Arnold Networks
KANs with learnable univariate spline activations on edges achieve better accuracy than MLPs with fewer parameters, faster scaling, and direct visualization for scientific discovery.
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On the Optimality of Reduced-Order Models for Band Structure Computations: A Kolmogorov $n$-Width Perspective
Kolmogorov n-widths of band structure solution manifolds decay exponentially with the minimum spectral gap, establishing sharp optimality bounds for linear reduced-order models.