基于KAN与动态上采样器的流场预测模型

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

计算物理 ›› 2024, Vol. 41 ›› Issue (6): 804-813.DOI: 10.19596/j.cnki.1001-246x.8988

基于KAN与动态上采样器的流场预测模型

常绍波¹(), 陈泽伟¹, 余建庚², 刘子扬¹, 陈刚¹^,*()

1. 西安交通大学航天航空学院复杂服役环境重大装备结构强度与寿命全国重点实验室, 陕西西安 710049
2. 航天通信控股集团股份有限公司, 浙江杭州 310009

收稿日期:2024-07-17 出版日期:2024-11-25 发布日期:2024-12-26
通讯作者: 陈刚
作者简介:
常绍波, 硕士研究生, 研究方向为深度学习在航空航天的应用, E-mail: 19935865264@163.com
基金资助:
国家自然科学基金(92371201); 国家自然科学基金(52192633); 国家自然科学基金(11872293); 陕西省杰出青年基金(2022JC-03)

Flow Field Prediction Model Based on KAN and Dynamic Upsample

Shaobo CHANG¹(), Zewei CHEN¹, Jiangeng YU², Ziyang LIU¹, Gang CHEN¹^,*()

1. National Key Laboratory of Structural Strength and Life of Major Equipment in Complex Service Environment, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, China
2. Aerospace Communications Holdings, Co., Ltd., Hangzhou, Zhejiang 310009, China

Received:2024-07-17 Online:2024-11-25 Published:2024-12-26
Contact: Gang CHEN

摘要/Abstract

摘要：

针对流场预测需求, 本文提出一种结合科尔莫哥罗夫-阿诺德网络(KAN)与动态上采样器(DySample: Upsampling by Dynamic Sampling)的KAN耦合模型(KADS), 并利用二维菱形翼型数据开展流场数据预测应用。本文改变原始KAN的激活函数B-Spline, 构建FourierKAN、GRBFKAN、RBFKAN、ChebyKAN等KAN结构, 并对其耦合DySample后的性能进行评估。通过与传统的多层感知机(MLP)进行对比发现, 以切比雪夫多项式为激活函数的ChebyKAN能以较少的训练时间和次数实现较高的准确率, 且在测试时不会出现过拟合的现象。结果表明: 本文提出的KADS模型适用于流场预测分析任务, 能够为深度学习流体智能建模提供新的建模方法与思路。

关键词: Kolmogorov-Arnold networks, 动态上采样器, 神经网络, 流场预测

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

常绍波, 陈泽伟, 余建庚, 刘子扬, 陈刚. 基于KAN与动态上采样器的流场预测模型[J]. 计算物理, 2024, 41(6): 804-813.

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.

图/表 10

图1 KAN网络架构示意图

Fig.1 Framework of KAN

图2 KADS网络架构图

Fig.2 Framework of KADS

图3 流场预测流程

Fig.3 Process of the prediction of flow field

表1 激活函数

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	$S_i(x)=a_i+b_i\left(x-x_i\right)+c_i\left(x-x_i\right)^2+d_i\left(x-x_i\right)^3$

图4 不同激活函数下的损失值

Fig.4 Loss values for different activation function

图5 ChebyKAN中(a)压力场p、(b)弦向速度场u、(c)法向速度场v的R2分布; MLP中(d)压力场p、(e)弦向速度场u、(f)法向速度场v的R2分布

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

图6 ChebyKAN中(a)p、(b) u、(c) v的相对误差RE和MLP中(d)p、(e) u、(f) v的相对误差RE

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

图7 CFD计算与KADS预测结果及误差图(a)KADS, 压力场；(b)CFD，压力场；(c)KADS和CFD计算结果误差(压力场p)；(d)KADS，速度场u；(e)CFD，速度场u; (f)KADS和CFD计算结果误差(速度场 u)；(g)KADS, 速度场 v; (h)CFD，速度场v；(i)KADS和CFD计算结果误差(速度场 v)

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)

图8 CFD与KADS预测结果及误差图(AOA=7.5°, Ma=11)

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

图9 CFD计算与MLP预测结果及误差图(AOA=7.5°, Ma=11)

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

参考文献 11

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基于KAN与动态上采样器的流场预测模型

Flow Field Prediction Model Based on KAN and Dynamic Upsample

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