Multifidelity Kolmogorov-Arnold Networks
This addresses a data efficiency problem for researchers and practitioners using KANs in domains like physics simulation, but it appears incremental as it builds on existing KAN methods.
The paper tackles the problem of reducing the need for expensive high-fidelity data in training Kolmogorov-Arnold networks (KANs) by developing multifidelity KANs (MFKANs) that use low-fidelity models and small amounts of high-fidelity data, resulting in accurate and robust predictions with less data and improved accuracy for physics-informed KANs without training data.
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.