DeepOKAN: Deep operator network based on Kolmogorov Arnold networks for mechanics problems

Diab W. Abueidda, Panos Pantidis, Mostafa E. Mobasher

Research output: Contribution to journalArticlepeer-review

Abstract

The modern digital engineering design often requires costly repeated simulations for different scenarios. The prediction capability of neural networks (NNs) makes them suitable surrogates for providing design insights. However, only a few NNs can efficiently handle complex engineering scenario predictions. We introduce a new version of the neural operators called DeepOKAN, which utilizes Kolmogorov Arnold networks (KANs) rather than the conventional neural network architectures. Our DeepOKAN uses Gaussian radial basis functions (RBFs) rather than the B-splines. RBFs offer good approximation properties and are typically computationally fast. The KAN architecture, combined with RBFs, allows DeepOKANs to represent better intricate relationships between input parameters and output fields, resulting in more accurate predictions across various mechanics problems. Specifically, we evaluate DeepOKAN's performance on several mechanics problems, including 1D sinusoidal waves, 2D orthotropic elasticity, and transient Poisson's problem, consistently achieving lower training losses and more accurate predictions compared to traditional DeepONets. This approach should pave the way for further improving the performance of neural operators.

Original languageEnglish (US)
Article number117699
JournalComputer Methods in Applied Mechanics and Engineering
Volume436
DOIs
StatePublished - Mar 1 2025

Keywords

  • Computational solid mechanics
  • Deep operator networks
  • Gaussian radial basis functions
  • Neural networks
  • Orthotropic elasticity
  • Transient analysis

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • General Physics and Astronomy
  • Computer Science Applications

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