DeepOKAN: Deep Operator Network Based on Kolmogorov Arnold Networks for Mechanics Problems

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. The DeepOKAN is used to develop surrogates for different mechanics problems. This approach should pave the way for further improving the performance of neural operators. Based on the current investigations, we observe that DeepOKANs require a smaller number of learnable parameters than current MLP-based DeepONets to achieve comparable accuracy.