Solutions to Two- and Three-Dimensional Incompressible Flow Fields Leveraging a Physics-Informed Deep Learning Framework and Kolmogorov-Arnold Networks

Physics-informed neural network (PINN) has become a potential technology for fluid dynamics simulations, but traditional PINN has low accuracy in simulating incompressible flows, and these problems can lead to PINN not converging. This paper proposes a physics-informed neural network method (KA-PINN) based on the Kolmogorov-Arnold Neural (KAN) network structure. It is used to solve two-dimensional and three-dimensional incompressible fluid dynamics problems. The flow field is reconstructed and predicted for the two-dimensional Kovasznay flow and the three-dimensional Beltrami flow. The results show that the prediction accuracy of KA-PINN is improved by about 5 times in two dimensions and 2 times in three dimensions compared with the fully connected network structure of PINN. Meanwhile, the number of network parameters is reduced by 8 to 10 times. The research results not only verify the application potential of KA-PINN in fluid dynamics simulations, but also demonstrate the feasibility of KAN network structure in improving the ability of PINN to solve and predict flow fields. This study can reduce the dependence on traditional numerical methods for solving fluid dynamics problems.