摘要
基于物理信息核函数神经网络技术,研究了梁板弯曲正、逆问题神经网络算法.该网络模型是引入两个不同物理信息核函数的独立网络,核函数中心位置由网络模型自适应配点,提高了计算的灵活性.由于激活函数包含微分方程的物理信息,无需对求解域进行离散,有效降低了计算成本.提出一种基于Galerkin等效的特解求解方法,可处理不连续源项,从而降低了求解难度.数值结果验证了所提方法在求解梁板弯曲正、逆问题上的有效性.该神经网络模型结构简单、求解形式灵活,可为求解力学问题和其他领域的(偏)微分方程中的神经网络结构设计提供参考.
Based on the technique of physics-informed kernel function neural network,a neural network method is proposed to solve the forward/inverse bending problems of beams and plates.This model includes two independent neural networks with different physics-informed kernel functions,and can achieve adaptive collocation by the neural network itself,which enhances the computational adaptability.Since the activation function includes the physical information of the differential governing equation,it is not necessary to consider the collocation nodes in the considered domain,which may effectively decrease the computational cost.A Galerkin equivalent method is presented to solve the particular solution for the discontinuous source term,which can reduce the difficulty in the training process.Numerical examples are given to verify the effectiveness in solving the the forward and inverse bending problems of beams and plates.This neural network has simple structure and flexible solution form,which can be applied to solve the problems of mechanics and(partial)differential equation in other fields.
作者
孙远航
蒋泉
陈巨兵
SUN Yuanhang;JIANG Quan;CHEN Jubing(School of Transportation and Civil Engineering,Nantong University,Nantong 226019,Jiangsu,China;School of Mathematics and Statistics,Nantong University,Nantong 226019,Jiangsu,China;School of Naval Architecture,Ocean and Civil Engineering,Shanghai Jiaotong University,Shanghai 200240,China)
出处
《力学季刊》
北大核心
2025年第2期327-339,共13页
Chinese Quarterly of Mechanics
基金
国家自然科学基金(12327802)
航空航天结构力学及控制全国重点实验室开放课题(MCAS-E-0124G01)。
