Multifidelity Kolmogorov-Arnold Networks

2024/10/18 by Amanda A. Howard, Howard, Amanda A., Bruno Jacob +3 · 3 citations
Computer Science · #Cognitive Computing and Networks #Computability, Logic, AI Algorithms #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2410.14764

openalex publication_date 2024/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

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.

Cited by

• Bridging quantum and classical computing for partial differential equations through multifidelity machine learning
• A Practitioner's Guide to Kolmogorov-Arnold Networks
• Training Deep Physics-Informed Kolmogorov-Arnold Networks

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