Computational Mechanics with Neural Networks

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