基于机器学习的Kelvin源格林函数数值预报  

Numerical prediction of Kelvin source Green’s function based on machine learning

作　　者：周子轩 朱仁传[1,2] 詹可 ZHOU Zixuan;ZHU Renchuan;ZHAN Ke(School of Ocean and Civil Engineering,Shanghai Jiao Tong University,Shanghai 200240,China;State Key Laboratory of Ocean Engineering,Shanghai Jiao Tong University,Shanghai 200240,China)

机构地区：[1]上海交通大学船舶海洋与建筑工程学院,上海200240 [2]上海交通大学海洋工程全国重点实验室,上海200240

出　　处：《海洋工程》2025年第2期170-178,共9页The Ocean Engineering

基　　金：国家自然科学基金资助项目(U2141228)。

摘　　要：快速、准确地计算Kelvin源格林函数及其偏导数是求解船舶移动兴波问题的基础及核心,其主要困难源于远场波动项积分核的高频振荡。鉴于机器学习理论中多层感知机(multilayer perceptron,简称MLP)的强大非线性映射能力,构建了针对Kelvin源格林函数及其偏导数的MLP数值预报模型。模型训练及测试所需的高精度数据样本均由自适应积分方法生成。为了充分利用样本信息,降低训练耗时,提出了一种基于收敛函数的创新采样策略,实现对近自由面区域的局部加密采样。数值分析结果表明,MLP模型预报精度良好,且效率显著优于自适应积分等数值方法。该模型不仅在兴波问题求解中有重要应用价值,也为机器学习在传统水动力领域的应用开辟了新的思路。The rapid and accurate computation of the Kelvin source Green’s function and its partial derivatives is fundamental and central to solving the ship motion wave-making problem.The primary challenge lies in the high-frequency oscillations of the far-field wave component’s integral kernel.Given the strong nonlinear mapping capability of multilayer perceptrons(MLP)in machine learning theory,an MLP-based numerical prediction model for the Kelvin source Green’s function and its partial derivatives is developed.High-precision data samples required for model training and testing are generated using an adaptive integration method.To fully exploit sample information and reduce training time,an innovative convergence-function-based sampling strategy is proposed to achieve local refinement sampling near the free surface region.Numerical analysis results indicate that the MLP model demonstrates excellent prediction accuracy and significantly outperforms numerical methods such as adaptive integration in terms of efficiency.This model not only has significant application value in solving wave-making problems but also opens new avenues for applying machine learning in traditional hydrodynamics.

关 键 词：Kelvin源格林函数 远场波动项 高频振荡 多层感知机 

分 类 号：P751[交通运输工程—港口、海岸及近海工程]