Computational mechanics with deep learning : an introduction

著者

• 矢川, 元基 ヤガワ, ゲンキ
• Oishi, Atsuya

書誌事項

Computational mechanics with deep learning : an introduction

Genki Yagawa, Atsuya Oishi

（Lecture notes on numerical methods in engineering and sciences）

Springer, c2023

注記

Includes bibliographical references and index

内容説明・目次

内容説明

This book is intended for students, engineers, and researchers interested in both computational mechanics and deep learning. It presents the mathematical and computational foundations of Deep Learning with detailed mathematical formulas in an easy-to-understand manner. It also discusses various applications of Deep Learning in Computational Mechanics, with detailed explanations of the Computational Mechanics fundamentals selected there. Sample programs are included for the reader to try out in practice. This book is therefore useful for a wide range of readers interested in computational mechanics and deep learning.

目次

Preface Part I Fundamentals 1 Overview 1.1 Deep Learning: New Way for Problems Unsolvable by Conventional Methods 1.2 Progress of Deep Learning: From McCulloch-Pitts Model to Deep Learning 1.3 New Techniques for Deep Learning References 2 Mathematical Background for Deep Learning 2.1 Feedforward Neural Network 2.2 Convolutional Neural Network 2.3 Training Acceleration 2.4 Regularization References 3 Computational Mechanics with Deep Learning 3.1 Overview 3.2 Recent Papers on Computational Mechanics with Deep Learning References Part II Case Study 4 Numerical Quadrature with Deep Learning 4.1 Summary of Numerical Quadrature 4.2 Summary of Stiffness Matrix for Finite Element Method 4.3 Accuracy Dependency of Stiffness Matrix on Numerical Quadrature 4.4 Search for Optimal Quadrature Parameters 4.5 Search for Optimal Number of Quadrature Points 4.6 Deep Learning for Optimal Quadrature of Element Stiffness Matrix 4.7 Numerical Example A 4.8 Numerical Example B References 5 Improvement of Finite Element Solutions with Deep Learning 5.1 Accuracy vs. Element Size 5.2 Computation Time vs. Element Size 5.3 Error Estimation of Finite Element Solutions 5.4 Improvement of Finite Element Solutions Using Error Information and Deep Learning 5.5 Numerical Example References 6 Contact Mechanics with Deep Learning 6.1 Basics of Contact Mechanics 6.2 NURBS Basis Functions 6.3 NURBS Objects based on NURBS Basis Functions 6.4 Local Contact Search for Surface-to-Surface Contact 6.5 Local Contact Search with Deep Learning 6.6 Numerical Example References 7 Flow Simulation with Deep Learning 7.1 Equations for Flow Simulation 7.2 Finite Difference Approximation 7.3 Flow Simulation of Incompressible Fluid with Finite Difference Method 7.4 Flow Simulation with Deep Learning 7.5 Neural Networks for Time-dependent Data 7.6 Numerical Example References 8 Further Applications with Deep Learning 8.1 Deep Learned Finite Elements 8.2 FEA-Net 8.3 DiscretizationNet 8.4 Zooming Method for Finite Element Analysis 8.5 Physics-informed Neural Network References Part III Computational Procedures 9 Bases for Computer Programming 9.1 Computer Programming for Data Preparation Phase 9.2 Computer Programming for Training Phase References 10 Computer Programming for a Representative Problem 10.1 Problem Definition 10.2 Data preparation Phase 10.3 Training Phase 10.4 Application Phase References

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詳細情報

• NII書誌ID(NCID): BC18652214
• ISBN:
  • 9783031118463
• 出版国コード: sz
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Cham
• ページ数/冊数: xiv, 402 p.
• 大きさ: 25 cm
• 分類:
  • DC23 : 620.100285631
• 件名:
  • LCSH : Mechanics, Applied -- Data processing
  • LCSH : Deep learning (Machine learning)
• 親書誌ID:
  • BA91191925