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

IF 2.9 3区工程技术 Q2 ENGINEERING, CIVIL

Frontiers of Structural and Civil Engineering Pub Date : 2024-09-03 DOI:10.1007/s11709-024-1011-4

Abhishek Mishra, Cosmin Anitescu, Pattabhi Ramaiah Budarapu, Sundararajan Natarajan, Pandu Ranga Vundavilli, Timon Rabczuk

引用次数: 0

Abstract

A combined deep machine learning (DML) and collocation based approach to solve the partial differential equations using artificial neural networks is proposed. The developed method is applied to solve problems governed by the Sine–Gordon equation (SGE), the scalar wave equation and elasto-dynamics. Two 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 integration. The methodology is implemented using the Tensorflow framework and it is tested on several numerical examples. Based on the results, the relative normalized error was observed to be less than 5% in all cases.

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基于人工神经网络的深度配位法求解瞬态线性和非线性偏微分方程

本文提出了一种基于深度机器学习（DML）和搭配的组合方法，利用人工神经网络求解偏微分方程。所开发的方法适用于解决正弦-戈登方程（SGE）、标量波方程和弹性力学问题。研究了两种方法：一种是时空公式，另一种是基于隐式 Runge-Kutta (RK) 时间积分的半离散方法。该方法使用 Tensorflow 框架实现，并在几个数值示例中进行了测试。结果表明，在所有情况下，相对归一化误差均小于 5%。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Frontiers of Structural and Civil Engineering Engineering-Architecture

CiteScore

5.20

自引率

3.30%

发文量

734

期刊介绍： Frontiers of Structural and Civil Engineering is an international journal that publishes original research papers, review articles and case studies related to civil and structural engineering. Topics include but are not limited to the latest developments in building and bridge structures, geotechnical engineering, hydraulic engineering, coastal engineering, and transport engineering. Case studies that demonstrate the successful applications of cutting-edge research technologies are welcome. The journal also promotes and publishes interdisciplinary research and applications connecting civil engineering and other disciplines, such as bio-, info-, nano- and social sciences and technology. Manuscripts submitted for publication will be subject to a stringent peer review.