KKANs, a two-block KART-based architecture with MLP inner functions and basis-function outer functions, universally approximate continuous functions and empirically outperform MLP and cKAN baselines in regression, PINN, and operator-learning benchmarks.
Multifidelity Kolmogorov-Arnold Networks
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abstract
We develop a method for multifidelity Kolmogorov-Arnold networks (KANs), which use a low-fidelity model along with a small amount of high-fidelity data to train a model for the high-fidelity data accurately. Multifidelity KANs (MFKANs) reduce the amount of expensive high-fidelity data needed to accurately train a KAN by exploiting the correlations between the low- and high-fidelity data to give accurate and robust predictions in the absence of a large high-fidelity dataset. In addition, we show that multifidelity KANs can be used to increase the accuracy of physics-informed KANs (PIKANs), without the use of training data.
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KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics
KKANs, a two-block KART-based architecture with MLP inner functions and basis-function outer functions, universally approximate continuous functions and empirically outperform MLP and cKAN baselines in regression, PINN, and operator-learning benchmarks.