Structure-Preserving Recurrent Neural Networks for a Class of Birkhoffian Systems

作     者：XIAO Shanshan CHEN Mengyi ZHANG Ruili TANG Yifa XIAO Shanshan;CHEN Mengyi;ZHANG Ruili;TANG Yifa

作者机构：LSECICMSECAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical SciencesUniversity of Chinese Academy of SciencesBeijing 100049China School of Mathematics and StatisticsBeijing Jiaotong UniversityBeijing 100044China 

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：441-462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] 070102[理学-计算数学] 0835[工学-软件工程] 0701[理学-数学] 0811[工学-控制科学与工程] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：supported by the National Natural Science Foundation of China under Grant Nos.12171466 and 12271025 

主　　题：Birkhoffian system k(z,t)-symplectic neural networks recurrent neural network 

摘      要：In this paper,the authors propose a neural network architecture designed specifically for a class of Birkhoffian systems—The Newtonian *** proposed model utilizes recurrent neural networks(RNNs)and is based on a mathematical framework that ensures the preservation of the Birkhoffian *** authors demonstrate the effectiveness of the proposed model on a variety of problems for which preserving the Birkhoffian structure is important,including the linear damped oscillator,the Van der Pol equation,and a high-dimensional *** with the unstructured baseline models,the Newtonian neural network(NNN)is more data efficient,and exhibits superior generalization ability.