Lecture Notes on Numerical Methods in Engineering and Scienc

Part I Preliminaries: Machine Learning Technologies for Computational Mechanics1. Computers and Network1.1 Computers and Processors1.2 Network Technologies1.3 Parallel Processing1.4 Numerical Precision2. Feedforward Neural Networks2.1 Bases2.2 Various Types of Layers2.3 Regularization2.4 Acceleration for Training2.5 Initialization of Connection Weights2.6 Model Averaging and Dropout3. Deep Learning3.1 Neural Network vs. Deep Learning3.2 Pretraining: Autoencoder3.3 Pretraining: Restricted Boltzmann Machine4. Mutually Connected Neural Networks4.1 Hopfield Network4.2 Boltzmann Machine5. Other Neural Networks5.1 Self-Organizing Maps5.2 Radial Basis Function Networks6. Other Algorithms and Systems6.1 Genetic Algorithms6.2 Genetic Programming6.3 Other Bio-inspired Algorithms6.4 Support Vector Machines6.5 Expert Systems6.6 Software ToolsPart II Applications27. Introductory Remarks8. Constitutive Models8.1 Parameter Determination of Viscoplastic Constitutive Equations8.2 Implicit Constitutive Modelling for Viscoplasticity8.3 Autoprogressive Algorithm8.4 Others9. Numerical Quadrature9.1 Optimization of Number of Quadrature Points9.2 Optimization of Quadrature Parameters10. Identifications of Analysis Parameters10.1 Time Step Evaluation of Pseudo Time-dependent Stress Analysis10.2 Parameter Identification of Augmented Lagrangian Method10.3 Predictor-Corrector Method for Structural Nonlinear Analysis10.4 Contact Stiffness Estimation11. Solvers and Solution Methods11.1 Finite Element Solutions through Direct Minimization of Energy Functionals11.2 Neurocomputing Model for Elastoplasticity11.3 Structural Re-analysis11.4 Simulations of Global Flexibility and Element Stiffness11.5 Solutions based on Variational Principle11.6 Boundary Conditions11.7 Hybrid Graph-Neural Method for Domain Decomposition11.8 Wavefront Reduction11.9 Contact Search11.10 Physics-informed Neural Networks11.11 Dynamic Analysis with Explicit Time Integration Scheme11.12 Reduced Order Model for Improvement of Solutions using Coarse Mesh12. Structural Identification12.1 Identification of Defects with Laser Ultrasonics12.2 Identification of Cracks12.3 Estimation of Stable Crack Growth12.4 Failure Mechanisms in Power Plant Components12.5 Identification of Parameters of Non-uniform Beam12.6 Prediction of Beam-Mass Vibration12.7 Others12.7.1 Nondestructive Evaluation with Neural Networks12.7.2 Structural Identification with Neural Networks312.7.3 Neural Networks Combined with Global Optimization Method12.7.4 Training of Neural Networks13. Structural Optimization13.1 Hole Image Interpretation for Integrated Topology and Shape Optimization13.2 Preform Tool Shape Optimization and Redesign13.3 Evolutionary Methods for Structural Optimization with Adaptive Neural Networks13.4 Optimal Design of Materials13.5 Optimization of Production Process13.6 Estimation and Control of Dynamic Behaviors of Structures13.7 Subjective Evaluations for Handling and Stability of Vehicle13.8 Others14. Some Notes on Applications of Neural Networks to Computational Mechanics14.1 Comparison among Neural Networks, and Other AI Technologie