Flow-dynamics informed Kolmogorov–Arnold networks for simulating subsonic compressible flow around airfoils

Deep learning has been probed for surrogate modeling of flow around airfoils. While physics-informed neural networks (PINNs) built on sparse data possess some physical interpretability, the prediction of flow fields may deviate from the true distribution. Moreover, the complex interactions among numerous parameters and layer nodes in traditional multi-layer perceptrons further limit interpretability. To ensure the credibility of predictions, this paper proposes flow-dynamics informed Kolmogorov–Arnold networks (FDIKANs) to simulate subsonic compressible unsteady flow fields around airfoils developed by the National Advisory Committee for Aeronautics. The proposed framework embeds flow dynamics implied by the Euler equations into small datasets and shows potential in interpretable symbolic regression through learnable nonlinear activation functions. The scalability of Kolmogorov–Arnold networks (KANs) enables using different variants, for which we specify FDIKANs with Skip connections and Radial Basis Functions (SRBFs). Compared to vanilla KANs, FDIKANs with SRBFs reduce model parameters by 70% and save training time by 90% (refer to Table I in Sec. IV B 1). Our method involves adaptive weight balancing and parameter-efficient structure search algorithms to improve training performance and determine the network structure. Experiments show that under different flow conditions, FDIKANs significantly outperform PINNs, reducing the prediction error of the density field representing compression effects by 30%. In addition, numerical simulation data validate the generalization capability of FDIKANs to unseen spatial domains and airfoils, indicating their potential as a promising tool for rapid and accurate prediction of detailed compressible unsteady flow fields.