Multifidelity Kolmogorov–Arnold networks

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 MFKANs can be used to increase the accuracy of physics-informed KANs, without the use of training data.