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.

翻译：现代数字化工程设计常需针对不同工况进行成本高昂的重复仿真。神经网络（NNs）的预测能力使其成为提供设计洞见的理想替代模型。然而，仅有少数神经网络能高效处理复杂工程场景的预测任务。本文提出一种新型神经算子架构DeepOKAN，其采用Kolmogorov Arnold网络（KANs）替代传统神经网络结构。我们的DeepOKAN使用高斯径向基函数（RBFs）而非B样条函数，并成功构建了多种力学问题的替代模型。该方法有望为提升神经算子性能开辟新路径。当前研究表明，相较于现有基于MLP的DeepONet，DeepOKAN仅需更少的可学习参数即可达到相当的精度。