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

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