A Deep Learning Method for Non-Uniform Flow Field Based on KAN and MLP Neural Networks

Fluid-solid interaction(FSI) has always been a hot topic in the field of fluid mechanics. Because the flow field of FSI is highly inhomogeneous, when the initial conditions change with time, the inhomogeneity of the flow field in time and space will be further aggravated. The forward and inverse solutions of physical information neural networks (PINNs) in fluid mechanics have been widely studied and significant progress has been made. The technology of learning and reconstructing the flow field with PINNs is relatively mature. However, there are still large errors in predicting the flow field with uneven temporal and spatial distribution. Neural networks(NN) cannot capture some local details in learning. In addition, the generalization characteristics of NNs will also weaken the learning of local highlight areas. Therefore, inspired by the confidence weight, this paper proposes a local reinforcement learning (LRL) method to solve the above problems. It is found that LRL has a good effect on local learning. Based on the LRL method, the applicability of three different NN frameworks in the reconstruction of FSI flow fields is tested, namely, multilayer perceptron(MLP), KAN and KAN + MLP. For the MLP framework, the details of the inhomogeneous flow field can be learned more accurately. For the KAN framework, by setting different depths and widths for NN, it is found that the prediction accuracy of KAN does not depend on the scale of NN, but has specific settings for specific problems. However, when applying the LRL method, the prediction effect of KAN is not particularly ideal, so the KAN + MLP framework is proposed as an improved method. The prediction effect is relatively ideal, but it takes a lot of time to train. In this study, the performance of the new framework KAN in inhomogeneous flow field is tested, which provides ideas and basis for further research on its application scope and practical effect in fluid mechanics.