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

TL;DR

This work tackles uncertainty quantification for Kolmogorov-Arnold Networks (KANs) in data-scarce scientific settings by coupling ensemble-based predictions with split conformal prediction to produce calibrated prediction intervals with coverage guarantees. The method, termed Conformalized-KANs, extends naturally to Finite Basis KANs (FBKANs) and Multi-Fidelity KANs (MFKANs), leveraging domain decomposition and multifidelity learning to improve robustness. Across 1D, 2D, multi-fidelity, and PDE-based experiments, Conformalized-KANs achieve the target coverage level $1-\alpha$ (with $\alpha=0.05$) while often yielding narrower intervals, especially for FBKANs, demonstrating reliable and sharper uncertainty quantification in SciML applications. The results highlight the practical impact of distribution-free UQ for KAN-based models, enabling more trustworthy predictions in data-limited scientific contexts.

Abstract

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. Building on this, we introduce Conformalized-KANs, which integrate conformal prediction, a distribution-free UQ technique, with KAN ensembles to generate calibrated prediction intervals with guaranteed coverage. Extensive 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 show that the conformal KAN predictions can be applied to recent extensions of KANs, including Finite Basis KANs (FBKANs) and multifideilty KANs (MFKANs). The results demonstrate the potential of our approaches to improve the reliability and applicability of KANs in scientific machine learning.

Figures (8)

• Figure 1: Schematic representation of the Conformalized-KANs framework. Calibration step: A dedicated calibration dataset is used to estimate the conformal quantile $\hat{q_\alpha}$ corresponding to a target miscoverage rate $\alpha$. Inference step: This quantile is then employed to construct prediction intervals that achieve the desired coverage.
• Figure 2: Conformalized prediction intervals generated on 1-D function test dataset, computed with an ensemble size of 4 and a target miscoverage rate of $\alpha = 0.05$.
• Figure 3: Conformalized prediction intervals generated by Conformalized-KANs and Conformalized-FBKANs on the 2-D function test dataset, computed with an ensemble size of 4 and a target miscoverage rate of $\alpha = 0.05$.
• Figure 4: Conformalized prediction intervals generated by ensemble MFKANs and Conformalized-MFKANs on the high-fidelity test dataset, computed with an ensemble size of 5 and a target miscoverage rate of $\alpha = 0.05$.
• Figure 5: Conformalized prediction intervals generated by Conformalized-KANs and Conformalized-FBKANs on the wave equation test dataset, computed with an ensemble size of 10 and a target miscoverage rate of $\alpha = 0.05$.