基于POD和KAN的三维球水滴收集系数快速预测

Efficient prediction of water droplet collection coefficient for 3D spheres using POD and KAN

  • 摘要: 准确预测水滴收集系数是结冰分析和防除冰系统设计中的关键步骤。本文提出了基于本征正交分解(proper orthogonal decomposition, POD)和科尔莫哥罗夫-阿诺德网络(Kolmogorov–Arnold networks, KAN)的快速预测模型(POD-KAN),用于精确预测三维球表面的水滴收集系数。首先利用POD方法提取水滴收集系数的本征模态以及相应的拟合系数。随后,构建以工况参数为输入、拟合系数为输出的KAN深度神经网络模型,实现水滴收集系数的快速预测。为提升模型的泛化能力,引入了水滴惯性参数,实现了不同直径球的水滴收集系数的快速计算。结果表明,本文提出的POD-KAN预测模型适用于三维球水滴收集系数预测任务,能快速预测水滴收集系数且具有较高的预测精度,平均绝对误差为3.386×10–4

     

    Abstract: The accurate prediction of water droplet collection coefficients is essential for icing analysis and the design of anti- and de-icing systems. Traditional high-fidelity numerical simulation methods, however, are often hindered by their computational complexity and time-intensive nature. Deep learning-based rapid prediction methods for water droplet collection coefficients present a promising avenue to address these challenges. In this study, we propose a fast prediction approach leveraging Proper Orthogonal Decomposition (POD) and Kolmogorov–Arnold Networks (KAN) to accurately predict water droplet collection coefficients on 3D spherical surfaces. Using the POD method, intrinsic modes and their corresponding fitting coefficients are extracted. A KAN-based deep learning model is then developed, mapping working condition parameters to fitting coefficients for efficient prediction. To further enhance model generalization, droplet inertia parameters are incorporated. Experimental results demonstrate that the proposed POD-KAN model is well-suited for predicting water droplet collection coefficients on 3D spheres, delivering rapid predictions with high accuracy, achieving an average absolute error of 3.386 × 10–4.

     

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