An artificial neural network based deep collocation method for the solution of transient linear and nonlinear partial differential equations

作     者：Abhishek MISHRA Cosmin ANITESCU Pattabhi Ramaiah BUDARAPU Sundararajan NATARAJAN Pandu Rang VUNDAVILLI Timon RABCZUK 

作者机构：School of Mechanical SciencesIndian Institute of TechnologyBhubaneswar 752050India Institute of Structural MechanicsBauhaus University of WeimarWeimar 99423Germany Department of Mechanical EngineeringIndian Institute of Technology MadrasChennai 600036India 

出 版 物：《Frontiers of Structural and Civil Engineering》 (结构与土木工程前沿（英文版）)

年 卷 期：2024年第18卷第8期

页      面：1296-1310页

核心收录：

学科分类：08[工学] 081402[工学-结构工程] 081304[工学-建筑技术科学] 0813[工学-建筑学] 0814[工学-土木工程] 

基　　金：the funds from the Department of Science and Technology(DST) Science and Engineering Research Board(SERB) India(No.SRG/2019/001581) 

主　　题：collocation method artificial neural networks deep machine learning Sine-Gordon equation transient wave equation dynamic scalar and elasto-dynamic equation Runge-Kutta method 

摘      要：A combined deep machine learning(DML)and collocation based approach to solve the partial differential equations using artificial neural networks is *** developed method is applied to solve problems governed by the Sine–Gordon equation(SGE),the scalar wave equation and *** methods are studied:one is a space-time formulation and the other is a semi-discrete method based on an implicit Runge–Kutta(RK)time *** methodology is implemented using the Tensorflow framework and it is tested on several numerical *** on the results,the relative normalized error was observed to be less than 5%in all cases.