{"title":"基于径向基函数神经网络的微分方程数值解","authors":"Liang Jianyu, Luo Siwei, Qi Yingjian, H. Yaping","doi":"10.1109/IJCNN.2002.1005571","DOIUrl":null,"url":null,"abstract":"In this paper we present a method for solving linear ordinary differential equations (ODE) based on multiquadric (MQ) radial basis function networks (RBFNs). According to the thought of approximation of function and/or its derivatives by using radial basis function networks, another new RBFN approximation procedures different from are developed in this paper for solving ODE. This technique can determine all the parameters at the same time without a learning process. The advantage of this technique is that it doesn't need sufficient data, just relies on the domain and the boundary. Our results are more accurate.","PeriodicalId":382771,"journal":{"name":"Proceedings of the 2002 International Joint Conference on Neural Networks. IJCNN'02 (Cat. No.02CH37290)","volume":"57 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2002-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"16","resultStr":"{\"title\":\"Numerical solution of differential equations by radial basis function neural networks\",\"authors\":\"Liang Jianyu, Luo Siwei, Qi Yingjian, H. Yaping\",\"doi\":\"10.1109/IJCNN.2002.1005571\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper we present a method for solving linear ordinary differential equations (ODE) based on multiquadric (MQ) radial basis function networks (RBFNs). According to the thought of approximation of function and/or its derivatives by using radial basis function networks, another new RBFN approximation procedures different from are developed in this paper for solving ODE. This technique can determine all the parameters at the same time without a learning process. The advantage of this technique is that it doesn't need sufficient data, just relies on the domain and the boundary. Our results are more accurate.\",\"PeriodicalId\":382771,\"journal\":{\"name\":\"Proceedings of the 2002 International Joint Conference on Neural Networks. IJCNN'02 (Cat. No.02CH37290)\",\"volume\":\"57 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2002-08-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"16\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the 2002 International Joint Conference on Neural Networks. IJCNN'02 (Cat. No.02CH37290)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/IJCNN.2002.1005571\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the 2002 International Joint Conference on Neural Networks. IJCNN'02 (Cat. No.02CH37290)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/IJCNN.2002.1005571","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Numerical solution of differential equations by radial basis function neural networks
In this paper we present a method for solving linear ordinary differential equations (ODE) based on multiquadric (MQ) radial basis function networks (RBFNs). According to the thought of approximation of function and/or its derivatives by using radial basis function networks, another new RBFN approximation procedures different from are developed in this paper for solving ODE. This technique can determine all the parameters at the same time without a learning process. The advantage of this technique is that it doesn't need sufficient data, just relies on the domain and the boundary. Our results are more accurate.