基于课程正则化的物理信息神经网络渐进式训练策略  

Progressive training strategy of physics-informed neural networks based on curriculum regularization

作　　者：范黎林[1] 刘士豪 李源[1,2] 毛文涛 陈宗涛[1] FAN Lilin;LIU Shihao;LI Yuan;MAO Wentao;CHEN Zongtao(College of Computer and Information Engineering,Henan Normal University,Xinxiang 453007,Henan,China;Engineering Lab of Intelligence Business&Internet of Things,Xinxiang 453007,Henan,China)

机构地区：[1]河南师范大学计算机与信息工程学院,河南新乡453007 [2]智慧商务与物联网技术河南省工程实验室,河南新乡453007

出　　处：《山东大学学报（工学版）》2024年第1期11-24,共14页Journal of Shandong University（Engineering Science）

基　　金：国家自然科学基金资助项目(11702087,U1704158);河南省科技攻关重点项目(212102210103)。

摘　　要：为降低物理信息神经网络(physics-informed neural networks,PINN)优化目标函数的复杂性和训练难度,提出一种基于课程正则化渐进式训练策略,在该策略中基于课程学习思想动态调整损失函数,使正则化项中偏微分方程所表征的物理信息从较平稳状态逐步过渡到变化剧烈状态,降低任务学习难度;加强损失函数中初始条件和边界条件部分的数据约束,平衡数据部分和物理信息部分损失;采用固定步长指数衰减学习率进行优化,尽可能避免目标函数陷入局部最小值。通过波动和热传导两类偏微分方程进行试验对比和分析,结果表明计算效率能够提升约50%,预测精度能够提高0.5~1个数量级。所提出方法可以有效提高PINN的数值稳定性和预测精度,加快PINN在复杂物理场学习任务中收敛速率。A progressive training strategy based on curriculum regularization was proposed to reduce the complexity and training difficulty of the optimization objective function for physics-informed neural networks(PINN).In this strategy,the loss function was dynamically adjusted based on the idea of course learning.The physical information represented by the partial differential equation in the regularization term was gradually transitioned from a relatively stable state to a drastic state,which reduced the learning difficulty of task.The data constraints of initial conditions and boundary conditions in the loss function were strengthened to balance the losses between the data and physical information parts.A fixed step-size exponential decay learning rate was employed for optimization to avoid the objective function falling into the local minimum.Through experimental comparison and analysis of two types of partial differential equations,namely wave and heat conduction,the results showed that the computational efficiency could be improved by about 50%,and the prediction accuracy can be improved by an order of magnitude.The proposed method could improve the numerical stability and prediction accuracy of PINN,and accelerate the convergence rate of PINN in complex physical field learning tasks.

关 键 词：物理信息神经网络 课程学习 损失函数 偏微分方程 数值稳定性 

分 类 号：TP181[自动化与计算机技术—控制理论与控制工程]