  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.
