mlsanityData to 14 Oct 2026

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

arXiv 2504.15240 ↗First posted 21 Apr 2025cs.LGcited by 3

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Abstract (arXiv)

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.

Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Builds on 38 of its 60 references that are in the map. First posted on arXiv 21 Apr 2025.

Builds on

38 of 60 references.

References · 38

  1. 2016Simple and Scalable Predictive Uncertainty Estimation using Deep Ensemblescited by 3,926
  2. 2021A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantificationcited by 792
  3. 2024KAN: Kolmogorov-Arnold Networkscited by 649
  4. 2019Conformalized Quantile Regressioncited by 629
  5. 2022Uncertainty Quantification in Scientific Machine Learning: Methods, Metrics, and Comparisonscited by 170
  6. 2021Finite Basis Physics-Informed Neural Networks (FBPINNs): a scalable domain decomposition approach for solving differential equationscited by 145
  7. 2024Wav-KAN: Wavelet Kolmogorov-Arnold Networkscited by 122
  8. 2024Chebyshev Polynomial-Based Kolmogorov-Arnold Networks: An Efficient Architecture for Nonlinear Function Approximationcited by 118
  9. 2024KAN 2.0: Kolmogorov-Arnold Networks Meet Sciencecited by 118
  10. 2024A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networkscited by 104
  11. 2024Kolmogorov-Arnold Networks (KANs) for Time Series Analysiscited by 98
  12. 2024DeepOKAN: Deep Operator Network Based on Kolmogorov Arnold Networks for Mechanics Problemscited by 84
26 more
  1. 2024KAN or MLP: A Fairer Comparisoncited by 73
  2. 2024TKAN: Temporal Kolmogorov-Arnold Networkscited by 71
  3. 2024fKAN: Fractional Kolmogorov-Arnold Networks with trainable Jacobi basis functionscited by 64
  4. 2024GKAN: Graph Kolmogorov-Arnold Networkscited by 53
  5. 2024Demonstrating the Efficacy of Kolmogorov-Arnold Networks in Vision Taskscited by 40
  6. 2022Scalable Uncertainty Quantification for Deep Operator Networks using Randomized Priorscited by 39
  7. 2024Adaptive Training of Grid-Dependent Physics-Informed Kolmogorov-Arnold Networkscited by 38
  8. 2024Finite basis Kolmogorov-Arnold networks: domain decomposition for data-driven and physics-informed problemscited by 35
  9. 2024Unveiling the Power of Wavelets: A Wavelet-based Kolmogorov-Arnold Network for Hyperspectral Image Classificationcited by 34
  10. 2024Suitability of KANs for Computer Vision: A preliminary investigationcited by 34
  11. 2024GraphKAN: Enhancing Feature Extraction with Graph Kolmogorov Arnold Networkscited by 32
  12. 2024Kolmogorov-Arnold Graph Neural Networkscited by 32
  13. 2022DeepONet-Grid-UQ: A Trustworthy Deep Operator Framework for Predicting the Power Grid's Post-Fault Trajectoriescited by 30
  14. 2024Conformalized-DeepONet: A Distribution-Free Framework for Uncertainty Quantification in Deep Operator Networkscited by 28
  15. 2024Physics Informed Kolmogorov-Arnold Neural Networks for Dynamical Analysis via Efficent-KAN and WAV-KANcited by 25
  16. 2024Inferring turbulent velocity and temperature fields and their statistics from Lagrangian velocity measurements using physics-informed Kolmogorov-Arnold Networkscited by 15
  17. 2024Kolmogorov-Arnold PointNet: Deep learning for prediction of fluid fields on irregular geometriescited by 12
  18. 2023Deep Operator Learning-based Surrogate Models with Uncertainty Quantification for Optimizing Internal Cooling Channel Rib Profilescited by 10
  19. 2024Multifidelity Kolmogorov-Arnold Networkscited by 9
  20. 2024Bayesian Kolmogorov Arnold Networks (Bayesian_KANs): A Probabilistic Approach to Enhance Accuracy and Interpretabilitycited by 8
  21. 2024KAN versus MLP on Irregular or Noisy Functionscited by 7
  22. 2024Conformalized Prediction of Post-Fault Voltage Trajectories Using Pre-trained and Finetuned Attention-Driven Neural Operatorscited by 5
  23. 2024Multifidelity domain decomposition-based physics-informed neural networks and operators for time-dependent problemscited by 4
  24. 2025On the study of frequency control and spectral bias in Wavelet-Based Kolmogorov Arnold networks: A path to physics-informed KANscited by 2
  25. 2024Uncertainty Quantification with Bayesian Higher Order ReLU KANscited by 1
  26. 2025MLPs and KANs for data-driven learning in physical problems: A performance comparisoncited by 1

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Cited by year

Citing papers per year: 2025: 3.

3 papers.

  1. 2025A Conformal Prediction Framework for Uncertainty Quantification in Physics-Informed Neural Networkscited by 5
  2. 2025Ensembling Pruned Attention Heads For Uncertainty-Aware Efficient Transformerscited by 5
  3. 2025Multi-Exit Kolmogorov-Arnold Networks: enhancing accuracy and parsimonycited by 4