Derives deterministic distance-aware error bounds for spline networks (including KANs) via bottom-up composition from individual spline neurons under higher-order Lipschitz conditions.
Deepokan: Deepoperatornetworkbasedonkolmogorovarnoldnetworksformechanics problems
3 Pith papers cite this work. Polarity classification is still indexing.
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The work introduces a modulation-based analytical method for singularity proofs in singular PDEs and refines ML techniques like PINNs and KANs to identify blowup solutions, with application to the open 3D Keller-Segel problem.
P1-KAN introduces a new KAN architecture with theoretical approximation guarantees that outperforms MLPs and prior KAN variants on irregular functions while matching spline KAN accuracy on smooth ones, demonstrated on hydraulic optimization.
citing papers explorer
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Distance-Aware Error for Spline Networks: A Bottom-Up Approach to Uncertainty
Derives deterministic distance-aware error bounds for spline networks (including KANs) via bottom-up composition from individual spline neurons under higher-order Lipschitz conditions.
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Singularity Formation: Synergy in Theoretical, Numerical and Machine Learning Approaches
The work introduces a modulation-based analytical method for singularity proofs in singular PDEs and refines ML techniques like PINNs and KANs to identify blowup solutions, with application to the open 3D Keller-Segel problem.
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P1-KAN: an effective Kolmogorov-Arnold network with application to hydraulic valley optimization
P1-KAN introduces a new KAN architecture with theoretical approximation guarantees that outperforms MLPs and prior KAN variants on irregular functions while matching spline KAN accuracy on smooth ones, demonstrated on hydraulic optimization.