An explicit budget allocation condition is derived for two-stage kernel-based operator learning, relating training set size, input observations, and output resolution, alongside a physics-informed online reconstruction extension.
Kernel-based Approximation Meth ods using MATLAB
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Adaptive RBF-KAN adds multiple radial basis kernels and LOOCV-based shape initialization to FastKAN, with benchmark tests on 2D functions showing kernel-specific advantages for smooth, discontinuous, and oscillatory cases.
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Kernel-based Operator Learning: Error Analysis, Budget Allocation, and a Physics-Informed Extension
An explicit budget allocation condition is derived for two-stage kernel-based operator learning, relating training set size, input observations, and output resolution, alongside a physics-informed online reconstruction extension.
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Adaptive RBF-KAN: A Comparative Evaluation of Dynamic Shape Parameters in Kolmogorov-Arnold Networks
Adaptive RBF-KAN adds multiple radial basis kernels and LOOCV-based shape initialization to FastKAN, with benchmark tests on 2D functions showing kernel-specific advantages for smooth, discontinuous, and oscillatory cases.