An Introduction to Programming Physics-Informed Neural Network-Based Computational Solid Mechanics

IF 1.4 4区工程技术 Q2 ENGINEERING, MULTIDISCIPLINARY International Journal of Computational Methods Pub Date : 2023-06-08 DOI:10.1142/s0219876223500135

Jinshuai Bai, Hyogu Jeong, C. P. Batuwatta-Gamage, Shusheng Xiao, Qingxia Wang, C. M. Rathnayaka, Laith Alzubaidi, Gui-Rong Liu, Yuantong Gu

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Abstract

Physics-informed neural network (PINN) has recently gained increasing interest in computational mechanics. This work extends the PINN to computational solid mechanics problems. Our focus will be on the investigation of various formulation and programming techniques, when governing equations of solid mechanics are implemented. Two prevailingly used physics-informed loss functions for PINN-based computational solid mechanics are implemented and examined. Numerical examples ranging from 1D to 3D solid problems are presented to show the performance of PINN-based computational solid mechanics. The programs are built via Python with TensorFlow library with step-by-step explanations and can be extended for more challenging applications. This work aims to help the researchers who are interested in the PINN-based solid mechanics solver to have a clear insight into this emerging area. The programs for all the numerical examples presented in this work are available at https://github.com/JinshuaiBai/PINN_Comp_Mech .

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编程物理导论——基于神经网络的计算固体力学

近年来，物理信息神经网络(PINN)在计算力学领域引起了越来越多的兴趣。这项工作将PINN扩展到计算固体力学问题。当固体力学的控制方程被实施时，我们的重点将放在各种公式和编程技术的研究上。在基于pup的计算固体力学中，实现并检验了两种常用的物理信息损失函数。给出了从一维到三维固体问题的数值实例，以展示基于pup的计算固体力学的性能。这些程序是通过Python和TensorFlow库构建的，并附有逐步解释，可以扩展到更具挑战性的应用程序。本工作旨在帮助对基于pup的固体力学求解器感兴趣的研究人员对这一新兴领域有一个清晰的认识。所有在这项工作中提出的数值例子的程序可在https://github.com/JinshuaiBai/PINN_Comp_Mech。

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

International Journal of Computational Methods ENGINEERING, MULTIDISCIPLINARY-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

3.30

自引率

17.60%

发文量

审稿时长

15 months

期刊介绍： The purpose of this journal is to provide a unique forum for the fast publication and rapid dissemination of original research results and innovative ideas on the state-of-the-art on computational methods. The methods should be innovative and of high scholarly, academic and practical value. The journal is devoted to all aspects of modern computational methods including mathematical formulations and theoretical investigations; interpolations and approximation techniques; error analysis techniques and algorithms; fast algorithms and real-time computation; multi-scale bridging algorithms; adaptive analysis techniques and algorithms; implementation, coding and parallelization issues; novel and practical applications. The articles can involve theory, algorithm, programming, coding, numerical simulation and/or novel application of computational techniques to problems in engineering, science, and other disciplines related to computations. Examples of fields covered by the journal are: Computational mechanics for solids and structures, Computational fluid dynamics, Computational heat transfer, Computational inverse problem, Computational mathematics, Computational meso/micro/nano mechanics, Computational biology, Computational penetration mechanics, Meshfree methods, Particle methods, Molecular and Quantum methods, Advanced Finite element methods, Advanced Finite difference methods, Advanced Finite volume methods, High-performance computing techniques.