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.
@article{arxiv.2410.14764,
title = {Multifidelity Kolmogorov-Arnold Networks},
author = {Amanda A. Howard and Bruno Jacob and Panos Stinis},
journal= {arXiv preprint arXiv:2410.14764},
year = {2024}
}