基于PINN的变截面压电半导体纤维力学特性研究

Investigation on Mechanical Properties of Piezoelectric Fiber with Variable Cross-Section Based on PINN

为了研究任意截面形状的压电半导体纤维的力学特性,提出了基于物理信息的神经网络模型,应用深度学习算法求解复杂的变系数偏微分方程。以变截面压电半导体纤维的静态拉伸为例,构造深度神经网络作为试函数,将其代入控制方程形成残差,并作为机器学习的加权损失函数,进而通过深度机器学习技术逼近数值解。研究结果表明:该方法具有广泛适用性,能够求解任意截面形状压电半导体材料的线性和非线性方程。

In order to investigate the mechanical properties of non-uniform piezoelectric semiconductor(PS) fiber,the physics-informed neural network model(PINN) is proposed in this paper,and a deep learning algorithm is applied to solve the partial differential equations with variable coefficients.Taking the static extension of PS fiber with variable cross-section as an example,a deep neural network is firstly established as a trial function,and then substituted into the governing equations of PS to form a residual and used as the weighted loss function for the machine learning.Then,the numerical solution is approximated through the deep machined learning.The research results indicate that the presented method has wide applicability,and can be used to solve the linear and non-linear governing equations of PS materials with arbitrary cross-section.