In order to meet the demand for flow field prediction, this paper proposes KAN coupling model (KADS) combining Kolmogorov-Arnold network (KAN) and dynamic upsample (DySample: Upsampling by Dynamic Sampling), and uses two-dimensional diamond-shaped airfoil data to carry out flow field data prediction applications. In this paper, the activation function of the original KAN B-Spline is changed, and the KAN structures such as FourierKAN, GRBFKAN, RBFKAN, ChebyKAN are constructed, and their performance after coupling with DySample is evaluated. By comparing with the traditional MLP, it is found that ChebyKAN with Chebyshev polynomial as the activation function can achieve high accuracy with less training time and times, and there will be no overfitting during the test. The results show that the KADS model proposed in this paper can be applied to the task of flow field prediction and analysis, and can provide new modeling methods and ideas for the deep learning fluid intelligence modeling task.

The topological properties of the delay-time reconstruction transformation of the forced Brusselator system are analysed by means of the Jacobian of the transformation. Topological properties depending on the delay time and on the conditional stability of a time series itself are discussed. The conditional Lyapunov exponent is used to judge whether a time series is good or bad. Results show that the choice of the embedding dimension by using saturation of system invariants is not appropriate.