信息工程大学学报2024，Vol.25Issue(3)：323-330,8.DOI:10.3969/j.issn.1671-0673.2024.03.011
基于PINN的Burgers方程求解模型
Solution Model of Burgers Equation Based on PINN
摘要
Abstract
The traditional numerical solution methods face the problems of dimension disaster and effi-ciency and accuracy balance,while the neural network solution method based on data-driven has the problems of training redundancy and inexplicability.To solve this problem,physical information neural networks(PINNs)pay attention to the physical prior knowledge implied in the training data,integrate the ability of neural networks to fit complex variables,and endow the traditional neural networks with the physical interpretability that is lacking.By applying the algorithm model,a solution model of Burg-ers equation based on PINN is proposed.The algorithm model imposes physical information con-straints during training,so it can use a small number of training samples to learn and predict the par-tial differential equation model distributed in the space-time domain.The experimental results show that in the case of 1+1 dimensional Burgers equation,compared with the classical machine learning al-gorithm,the proposed method can effectively catch the changes of the equation and simulate accu-rately,and can significantly shorten the simulation time compared with the finite difference method.Through comparative experiments on different network parameters,even under 10%noise damage,it can produce reasonable recognition accuracy,and the undetermined coefficient error of network ap-proximation equation is within 0.001.关键词
计算流体力学/深度学习/物理信息神经网络/Burgers方程Key words
computational fluid dynamics/deep learning/physical information neural network/burg-分类
信息技术与安全科学引用本文复制引用
骆炜杰,李芳,陈鑫..基于PINN的Burgers方程求解模型[J].信息工程大学学报,2024,25(3):323-330,8.基金项目
国家重点研发计划(2020YFB0204800) （2020YFB0204800）
