Computational Mechanics with Neural Networks (Lecture Notes on Numerical Methods in Engineering and Sciences)

✍ Scribed by Genki Yagawa, Atsuya Oishi

• Publisher: Springer
• Year: 2021
• Tongue: English
• Leaves: 233
• Category: Library

✦ Synopsis

This book shows how neural networks are applied to computational mechanics. Part I presents the fundamentals of neural networks and other machine learning method in computational mechanics. Part II highlights the applications of neural networks to a variety of problems of computational mechanics. The final chapter gives perspectives to the applications of the deep learning to computational mechanics.

✦ Table of Contents

Preface
References
Contents
Part IPreliminaries: Machine Learning Technologies for Computational Mechanics
1 Computers and Network
1.1 Computers and Processors
1.2 Network Technologies
1.3 Parallel Processing
1.4 Numerical Precision
References
2 Feedforward Neural Networks
2.1 Bases
2.2 Various Types of Layers
2.3 Regularization
2.4 Acceleration for Training
2.5 Initialization of Connection Weights
2.6 Model Averaging and Dropout
References
3 Deep Learning
3.1 Neural Network Versus Deep Learning
3.2 Pretraining: Autoencoder
3.3 Pretraining: Restricted Boltzmann Machine
References
4 Mutually Connected Neural Networks
4.1 Hopfield Network
4.2 Boltzmann Machine
References
5 Other Neural Networks
5.1 Self-organizing Maps
5.2 Radial Basis Function Networks
References
6 Other Algorithms and Systems
6.1 Genetic Algorithms
6.2 Genetic Programming
6.3 Other Bio-inspired Algorithms
6.4 Support Vector Machines
6.5 Expert Systems
6.6 Software Tools
References
Part IIApplications
7 Introductory Remarks
References
8 Constitutive Models
8.1 Parameter Determination of Viscoplastic Constitutive Equations
8.2 Implicit Constitutive Modelling for Viscoplasticity
8.3 Autoprogressive Algorithm
8.4 Others
References
9 Numerical Quadrature
9.1 Optimization of Number of Quadrature Points
9.2 Optimization of Quadrature Parameters
Reference
10 Identifications of Analysis Parameters
10.1 Time Step Determination of Pseudo Time-Dependent Stress Analysis
10.2 Parameter Identification of Augmented Lagrangian Method
10.3 Predictor–Corrector Method for Nonlinear Structural Analysis
10.4 Contact Stiffness Estimation
References
11 Solvers and Solution Methods
11.1 Finite Element Solutions Through Direct Minimization of Energy Functional
11.2 Neurocomputing Model for Elastoplasticity
11.3 Structural Re-analysis
11.4 Simulations of Global Flexibility and Element Stiffness
11.5 Solutions Based on Variational Principle
11.6 Boundary Conditions
11.7 Hybrid Graph-Neural Method for Domain Decomposition
11.8 Wavefront Reduction
11.9 Contact Search
11.10 Physics-Informed Neural Networks
11.11 Dynamic Analysis with Explicit Time Integration Scheme
11.12 Reduced Order Model for Improvement of Solutions Using Coarse Mesh
References
12 Structural Identification
12.1 Identification of Defects with Laser Ultrasonics
12.2 Identification of Cracks
12.3 Estimation of Stable Crack Growth
12.4 Failure Mechanisms in Power Plant Components
12.5 Identification of Parameters of Non-uniform Beam
12.6 Prediction of Beam-Mass Vibration
12.7 Others
12.7.1 Nondestructive Evaluation with Neural Networks
12.7.2 Structural Identification with Neural Networks
12.7.3 Neural Networks Combined with Global Optimization Method
12.7.4 Training of Neural Networks
References
13 Structural Optimization
13.1 Hole Image Interpretation for Integrated Topology and Shape Optimization
13.2 Preform Tool Shape Optimization and Redesign
13.3 Evolutionary Methods for Structural Optimization with Adaptive Neural Networks
13.4 Optimal Design of Materials
13.5 Optimization of Production Process
13.6 Estimation and Control of Dynamic Behaviors of Structures
13.7 Subjective Evaluation for Handling and Stability of Vehicle
13.8 Others
References
14 Some Notes on Applications of Neural Networks to Computational Mechanics
14.1 Comparison among Neural Networks and Other AI Technologies
14.2 Improvements of Neural Networks in Terms of Applications to Computational Mechanics
References
15 Other AI Technologies for Computational Mechanics
15.1 Parameter Identification of Constitutive Model
15.2 Constitutive Material Model by Genetic Programming
15.3 Data-Driven Analysis Without Material Modelling
15.4 Numerical Quadrature
15.5 Contact Search Using Genetic Algorithm
15.6 Contact Search Using Genetic Programming
15.7 Solving Non-linear Equation Systems Using Genetic Algorithm
15.8 Nondestructive Evaluation
15.9 Structural Optimization
15.10 Others
References
16 Deep Learning for Computational Mechanics
16.1 Neural Networks Versus Deep Learning
16.2 Applications of Deep Convolutional Neural Networks to Computational Mechanics
16.3 Applications of Deep Feedforward Neural Networks to Computational Mechanics
16.4 Others
References
Appendix
A1. Bases of Finite Element Method
A2. Parallel Processing for Finite Element Method
A3. Isogeometric Analysis
A4. Free Mesh Method
A5. Other Meshless Methods
A6. Inverse Problems
References
Uncited References