Conformalized-KANs: Uncertainty Quantification with Coverage Guarantees for Kolmogorov-Arnold Networks (KANs) in Scientific Machine Learning

This paper explores uncertainty quantification (UQ) methods in the context of Kolmogorov–Arnold Networks (KANs). We apply an ensemble approach to KANs to obtain a heuristic measure of UQ, enhancing interpretability and robustness in modeling complex functions. However, particularly in data-limited and complex scientific settings, ensemble-based uncertainty estimates, as is the case for many UQ methods, are sensitive to implicit distributional assumptions and do not provide formal coverage guarantees. Building on this, we develop conformalized-KANs, a conformal UQ framework for KANs that combines ensemble-based uncertainty estimates with split conformal prediction to generate calibrated prediction intervals with formal coverage guarantees. Numerical experiments are conducted to evaluate the effectiveness of these methods, focusing particularly on the robustness and accuracy of the prediction intervals under various hyperparameter settings. We further show that this framework extends naturally to recent KAN variants, including finite basis KANs and multi-fidelity KANs. The results demonstrate the potential of our approaches to improve the reliability and applicability of KANs in scientific machine learning.