mlsanityData to 14 Oct 2026

MLPs and KANs for data-driven learning in physical problems: A performance comparison

arXiv 2504.11397 ↗First posted 15 Apr 2025cs.LG physics.comp-phcited by 1

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Abstract (arXiv)

There is increasing interest in solving partial differential equations (PDEs) by casting them as machine learning problems. Recently, there has been a spike in exploring Kolmogorov-Arnold Networks (KANs) as an alternative to traditional neural networks represented by Multi-Layer Perceptrons (MLPs). While showing promise, their performance advantages in physics-based problems remain largely unexplored. Several critical questions persist: Can KANs capture complex physical dynamics and under what conditions might they outperform traditional architectures? In this work, we present a comparative study of KANs and MLPs for learning physical systems governed by PDEs. We assess their performance when applied in deep operator networks (DeepONet) and graph network-based simulators (GNS), and test them on physical problems that vary significantly in scale and complexity. Drawing inspiration from the Kolmogorov Representation Theorem, we examine the behavior of KANs and MLPs across shallow and deep network architectures. Our results reveal that although KANs do not consistently outperform MLPs when configured as deep neural networks, they demonstrate superior expressiveness in shallow network settings, significantly outpacing MLPs in accuracy over our test cases. This suggests that KANs are a promising choice, offering a balance of efficiency and accuracy in applications involving physical systems.

Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 28 of its 53 references that are in the map. First posted on arXiv 15 Apr 2025.

Builds on

28 of 53 references.

References · 28

  1. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,305
  2. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
  3. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 2,018
  4. 2018Relational inductive biases, deep learning, and graph networkscited by 1,360
  5. 2020Learning to Simulate Complex Physics with Graph Networkscited by 880
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  10. 2024A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networkscited by 104
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  12. 2024DeepOKAN: Deep Operator Network Based on Kolmogorov Arnold Networks for Mechanics Problemscited by 84
16 more
  1. 2022Deep transfer operator learning for partial differential equations under conditional shiftcited by 83
  2. 2024KAN or MLP: A Fairer Comparisoncited by 73
  3. 2023Sequential Deep Operator Networks (S-DeepONet) for Predicting Full-field Solutions Under Time-dependent Loadscited by 47
  4. 2024Demonstrating the Efficacy of Kolmogorov-Arnold Networks in Vision Taskscited by 40
  5. 2018Deep, Skinny Neural Networks are not Universal Approximatorscited by 38
  6. 2024GraphKAN: Enhancing Feature Extraction with Graph Kolmogorov Arnold Networkscited by 32
  7. 2024Kolmogorov-Arnold Graph Neural Networkscited by 32
  8. 2024Basis-to-Basis Operator Learning Using Function Encoderscited by 17
  9. 2023Graph Neural Network-based surrogate model for granular flowscited by 16
  10. 2022Neural operator learning of heterogeneous mechanobiological insults contributing to aortic aneurysmscited by 14
  11. 2024Deep Learning Alternatives of the Kolmogorov Superposition Theoremcited by 12
  12. 2024Leveraging KANs For Enhanced Deep Koopman Operator Discoverycited by 10
  13. 2019Scalable and modular material point method for large-scale simulationscited by 9
  14. 2024Learning Hidden Physics and System Parameters with Deep Operator Networkscited by 7
  15. 2022Physics-informed ConvNet: Learning Physical Field from a Shallow Neural Networkcited by 5
  16. 2025Orthogonal greedy algorithm for linear operator learning with shallow neural networkcited by 3

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Citing papers per year: 2025: 1.

1 paper.

  1. 2025Conformalized-KANs: Uncertainty Quantification with Coverage Guarantees for Kolmogorov-Arnold Networks (KANs) in Scientific Machine Learningcited by 3