Pre-Training Physics-Informed Neural Network with Mixed Sampling and Its Application in High-Dimensional Systems

作     者：LIU Haiyi ZHANG Yabin WANG Lei LIU Haiyi;ZHANG Yabin;WANG Lei

作者机构：School of Mathematics and PhysicsNorth China Electric Power UniversityBeijing 102206China School of Control and Computer EngineeringNorth China Electric Power UniversityBeijing 102206China 

出 版 物：《Journal of Systems Science & Complexity》 (系统科学与复杂性学报（英文版）)

年 卷 期：2024年第37卷第2期

页      面：494-510页

核心收录：

学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 081104[工学-模式识别与智能系统] 08[工学] 070104[理学-应用数学] 0835[工学-软件工程] 0811[工学-控制科学与工程] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

主　　题：High-dimensional systems mixed sampling nonlinear wave pre-training physics-informed neural network 

摘      要：Recently,the physics-informed neural network shows remarkable ability in the context of solving the low-dimensional nonlinear partial differential ***,for some cases of high-dimensional systems,such technique may be time-consuming and *** this paper,the authors put forward a pre-training physics-informed neural network with mixed sampling(pPINN)to address these *** based on the initial and boundary conditions,the authors design the pre-training stage to filter out the set of the misfitting points,which is regarded as part of the training points in the next *** authors further take the parameters of the neural network in Stage 1 as the initialization in Stage *** advantage of the proposed approach is that it takes less time to transfer the valuable information from the first stage to the second one to improve the calculation accuracy,especially for the high-dimensional *** verify the performance of the pPINN algorithm,the authors first focus on the growing-and-decaying mode of line rogue wave in the Davey-Stewartson I *** case is the accelerated motion of lump in the inhomogeneous Kadomtsev-Petviashvili equation,which admits a more complex evolution than the uniform *** exact solution provides a perfect sample for data experiments,and can also be used as a reference frame to identify the performance of the *** experiments confirm that the pPINN algorithm can improve the prediction accuracy and training efficiency well,and reduce the training time to a large extent for simulating nonlinear waves of high-dimensional equations.