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

作　　者：XIAO Shanshan CHEN Mengyi ZHANG Ruili TANG Yifa 

机构地区：[1]LSEC,ICMSEC,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China [2]School of Mathematical Sciences,University of Chinese Academy of Sciences,Beijing 100049,China [3]School of Mathematics and Statistics,Beijing Jiaotong University,Beijing 100044,China

出　　处：《Journal of Systems Science & Complexity》2024年第2期441-462,共22页系统科学与复杂性学报（英文版）

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

摘　　要：In this paper,the authors propose a neural network architecture designed specifically for a class of Birkhoffian systems—The Newtonian system.The proposed model utilizes recurrent neural networks(RNNs)and is based on a mathematical framework that ensures the preservation of the Birkhoffian structure.The 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 example.Compared with the unstructured baseline models,the Newtonian neural network(NNN)is more data efficient,and exhibits superior generalization ability.

关 键 词：BIRKHOFFIAN system k(z t)-symplectic NEURAL NETWORKS RECURRENT NEURAL network 

分 类 号：O241.8[理学—计算数学] TP183[理学—数学]