Computational Mechanics with Deep Learning

An Introduction
1. Auflage 2023
ISBN: 978-3-031-11849-4
Verlag: Springer International Publishing

Buch, Englisch, 402 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 703 g

Reihe: Lecture Notes on Numerical Methods in Engineering and Sciences

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.

Zielgruppe

Graduate

Autoren/Hrsg.

Oishi, Atsuya

Yagawa, Genki

Fachgebiete

• Technische Wissenschaften Maschinenbau | Werkstoffkunde Maschinenbau
• Mathematik | Informatik EDV | Informatik Informatik Künstliche Intelligenz

Inhaltsverzeichnis

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

Über Autor(innen)

Genki Yagawa received his Ph.D. from University of Tokyo in 1970. He became Professor at University of Tokyo in 1984 and Director and Professor at Center for Computational Mechanics Research of Toyo University in 2004. Currently, he is an Emeritus Professor at University of Tokyo and Toyo University, Chairman of Nuclear Safety Research Association, and Member of Science Council of Japan. His awards and honors include the Order of the Sacred Treasure, Gold Rays with Neck Ribbon endowed from His Majesty the Japanese Emperor, Japan Academy Prize, International Association for Computational Mechanics Award, Asia Pacific Association Computational Mechanics Zienkiewicz Medal, Prime Minister Award, Minister of Science and Technology Award, Toray Science and Technology Medal, Honorary Doctor Endowed from Iasi Technical University, and Fellow of International Association for Computational Mechanics, Japan Society for Industrial and Applied Mathematics, Japan Society for Simulation Technology and Atomic Energy Society of Japan.

Atsuya Oishi received his Ph.D. from University of Tokyo in 1996. He became Lecturer at University of Tokushima in 1997 and has been an Associate Professor at University of Tokushima since 2006. His awards include the outstanding paper award from Japan Society for Computational Engineering and Science and JACM fellow award from Japan Association for Computational Mechanics.