Flow Field Prediction Model Based on KAN and Dynamic Upsample

doi:10.19596/j.cnki.1001-246x.8988

Abstract

Abstract:

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.

Key words: Kolmogorov-Arnold networks, dynamic upsample, neural network, flow prediction

Shaobo CHANG, Zewei CHEN, Jiangeng YU, Ziyang LIU, Gang CHEN. Flow Field Prediction Model Based on KAN and Dynamic Upsample[J]. Chinese Journal of Computational Physics, 2024, 41(6): 804-813.

Figures/Tables 10

Fig.1 Framework of KAN

Fig.2 Framework of KADS

Fig.3 Process of the prediction of flow field

Table 1 Activation Function

类型	数学表达式
Chebyshev Polynomials	T_n(x)=cos(ncos^-1(x))
Gaussian RBF	$\phi(x, c)=\exp \left(-\frac{\|x-c\|^2}{2 \sigma^2}\right)$
Radial Basis Function	ϕ(x, c)=f(\|x-c\|)
B-Spline	$S_i(x)=a_i+b_i\left(x-x_i\right)+c_i\left(x-x_i\right)^2+d_i\left(x-x_i\right)^3$

Fig.4 Loss values for different activation function

Fig.5 Coefficient of determination R2 of (a) p, (b) u, (c)v in ChebyKAN and (d)p, (e) u, (f) v in MLP

Fig.6 Relative error RE of (a) p、(b) u、(c) v in ChebyKAN and (d)p、(e) u、(f) v in MLP

Fig.7 CFD calculations and KADS predictions, and error map of airfoil (a)KADS, p; (b) CFD, p; (c) error between KADS and CFD (p); (d)KADS, u; (e) CFD, u; (f)error between KADS and CFD (u); (g)KADS, v; (h)CFD, v; (i)error between KADS and CFD (v)

Fig.8 CFD calculations and KADS predictions, and error map of airfoil(AOA=7.5°, Ma=11)

Fig.9 CFD calculations and MLP predictions, and error map of airfoil(AOA=7.5°, Ma=11)

References 11

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