Multifidelity Kolmogorov-Arnold Networks

TL;DR

This paper introduces Multifidelity Kolmogorov-Arnold Networks (MFKANs), which leverage low- and high-fidelity data to improve modeling accuracy while reducing the need for expensive high-fidelity data, also enhancing physics-informed models.

Contribution

The paper presents a novel multifidelity approach for KANs that effectively combines low- and high-fidelity data, improving accuracy and robustness in modeling complex systems.

Findings

MFKANs require less high-fidelity data for accurate modeling.

MFKANs improve the accuracy of physics-informed KANs without additional training data.

Multifidelity methods exploit correlations between data fidelities for better predictions.

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.