mlsanityData to 7 Oct 2026

Multifidelity Kolmogorov-Arnold Networks

arXiv 2410.14764 ↗First posted 18 Oct 2024cs.LG cs.NA math.NAcited by 9

Not on the map. Why?

Abstract (arXiv)

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.

Key facts. Cited by 9 papers in the map (data through 7 Oct 2026). Builds on 55 of its 95 references that are in the map. First posted on arXiv 18 Oct 2024.

Builds on

55 of 95 references.

References · 55

  1. 2024KAN: Kolmogorov-Arnold Networkscited by 634
  2. 2021Physics-informed neural networks (PINNs) for fluid mechanics: A reviewcited by 470
  3. 2018Survey of multifidelity methods in uncertainty propagation, inference, and optimizationcited by 141
  4. 2024Wav-KAN: Wavelet Kolmogorov-Arnold Networkscited by 118
  5. 2024KAN 2.0: Kolmogorov-Arnold Networks Meet Sciencecited by 116
  6. 2024Chebyshev Polynomial-Based Kolmogorov-Arnold Networks: An Efficient Architecture for Nonlinear Function Approximationcited by 115
  7. 2024A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networkscited by 103
  8. 2024Kolmogorov-Arnold Networks (KANs) for Time Series Analysiscited by 97
  9. 2022Multifidelity deep neural operators for efficient learning of partial differential equations with application to fast inverse design of nanoscale heat transportcited by 92
  10. 2024DeepOKAN: Deep Operator Network Based on Kolmogorov Arnold Networks for Mechanics Problemscited by 82
  11. 2024Convolutional Kolmogorov-Arnold Networkscited by 76
  12. 2024KAN or MLP: A Fairer Comparisoncited by 71
38 more
  1. 2024TKAN: Temporal Kolmogorov-Arnold Networkscited by 70
  2. 2020Transfer learning based multi-fidelity physics informed deep neural networkcited by 68
  3. 2024Kolmogorov Arnold Informed neural network: A physics-informed deep learning framework for solving forward and inverse problems based on Kolmogorov Arnold Networkscited by 64
  4. 2024fKAN: Fractional Kolmogorov-Arnold Networks with trainable Jacobi basis functionscited by 60
  5. 2020Multi-fidelity Bayesian Neural Networks: Algorithms and Applicationscited by 59
  6. 2022Multifidelity Deep Operator Networks For Data-Driven and Physics-Informed Problemscited by 57
  7. 2024GKAN: Graph Kolmogorov-Arnold Networkscited by 52
  8. 2023Multi-stage Neural Networks: Function Approximator of Machine Precisioncited by 48
  9. 2024KAGNNs: Kolmogorov-Arnold Networks meet Graph Learningcited by 48
  10. 2024Kolmogorov-Arnold Network for Satellite Image Classification in Remote Sensingcited by 46
  11. 2024Demonstrating the Efficacy of Kolmogorov-Arnold Networks in Vision Taskscited by 39
  12. 2024Adaptive Training of Grid-Dependent Physics-Informed Kolmogorov-Arnold Networkscited by 37
  13. 2024Finite basis Kolmogorov-Arnold networks: domain decomposition for data-driven and physics-informed problemscited by 35
  14. 2024Exploring the Potential of Polynomial Basis Functions in Kolmogorov-Arnold Networks: A Comparative Study of Different Groups of Polynomialscited by 33
  15. 2024Suitability of KANs for Computer Vision: A preliminary investigationcited by 33
  16. 2024ReLU-KAN: New Kolmogorov-Arnold Networks that Only Need Matrix Addition, Dot Multiplication, and ReLUcited by 32
  17. 2021Multi-fidelity regression using artificial neural networks: efficient approximation of parameter-dependent output quantitiescited by 31
  18. 2024Kolmogorov-Arnold Graph Neural Networkscited by 31
  19. 2022Bi-fidelity Modeling of Uncertain and Partially Unknown Systems using DeepONetscited by 27
  20. 2020On transfer learning of neural networks using bi-fidelity data for uncertainty propagationcited by 26
  21. 2021Multifidelity Modeling for Physics-Informed Neural Networks (PINNs)cited by 25
  22. 2024A Benchmarking Study of Kolmogorov-Arnold Networks on Tabular Datacited by 25
  23. 2024Physics Informed Kolmogorov-Arnold Neural Networks for Dynamical Analysis via Efficent-KAN and WAV-KANcited by 25
  24. 2021Galerkin Neural Networks: A Framework for Approximating Variational Equations with Error Controlcited by 24
  25. 2023Stacked networks improve physics-informed training: applications to neural networks and deep operator networkscited by 21
  26. 2024FC-KAN: Function Combinations in Kolmogorov-Arnold Networkscited by 18
  27. 2021Transfer Learning on Multi-Fidelity Datacited by 17
  28. 2024Reduced Effectiveness of Kolmogorov-Arnold Networks on Functions with Noisecited by 17
  29. 2021Neural Network Training Using ℓ1-Regularization and Bi-fidelity Datacited by 16
  30. 2024SineKAN: Kolmogorov-Arnold Networks Using Sinusoidal Activation Functionscited by 15
  31. 2024Inferring turbulent velocity and temperature fields and their statistics from Lagrangian velocity measurements using physics-informed Kolmogorov-Arnold Networkscited by 15
  32. 2024Physics-Informed Kolmogorov-Arnold Networks for Power System Dynamicscited by 14
  33. 2023A multifidelity approach to continual learning for physical systemscited by 13
  34. 2024Higher-order-ReLU-KANs (HRKANs) for solving physics-informed neural networks (PINNs) more accurately, robustly and fastercited by 13
  35. 2022Use of Multifidelity Training Data and Transfer Learning for Efficient Construction of Subsurface Flow Surrogate Modelscited by 11
  36. 2024Kolmogorov-Arnold PointNet: Deep learning for prediction of fluid fields on irregular geometriescited by 11
  37. 2020Exploring the potential of transfer learning for metamodels of heterogeneous material deformationcited by 9
  38. 2023Feature-adjacent multi-fidelity physics-informed machine learning for partial differential equationscited by 8

50 most cited of 55 All 55 (JSON)

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 1; 2025: 6; 2026: 2.

9 papers.

  1. 2024A Survey on Kolmogorov-Arnold Networkcited by 67
  2. 2025A Practitioner's Guide to Kolmogorov-Arnold Networkscited by 16
  3. 2025asKAN: Active Subspace embedded Kolmogorov-Arnold Networkcited by 5
  4. 2025Leveraging KANs for Expedient Training of Multichannel MLPs via Preconditioning and Geometric Refinementcited by 4
  5. 2025Conformalized-KANs: Uncertainty Quantification with Coverage Guarantees for Kolmogorov-Arnold Networks (KANs) in Scientific Machine Learningcited by 3
  6. 2025Training Deep Physics-Informed Kolmogorov-Arnold Networkscited by 2
  7. 2025Bridging quantum and classical computing for partial differential equations through multifidelity machine learningcited by 1
  8. 2026YOLO with Kolmogorov-Arnold networks and vision-language foundation models for interpretable object detection with trustworthy multimodal AI in computer vision perceptioncited by 0
  9. 2026Sample-Efficiency of Kolmogorov-Arnold Networkscited by 0