Deep Learning-Based Forward Modeling and Inversion Techniques for Computational Physics Problems

Description

Cover Half Title Title Page Copyright Page Dedication Contents Preface Symbols 1. Deep Learning Framework and Paradigm in Computational Physics 1.1. Traditional Numerical Algorithms 1.1.1. Moment of Method 1.1.2. Monte Carlo Method 1.2. Basic Neural Network Structure 1.2.1. Fully Connected Neural Network 1.2.2. Convolutional Neural Network 1.2.3. Recurrent Neural Network 1.2.4. Generative Adversarial Network 1.3. Paradigms in Deep Learning 1.3.1. Data Driven 1.3.2. Physics Constraint 1.3.2.1. Fully Connected Based PINN 1.3.2.2. Convolutional Based PINN 1.3.2.3. Recurrent Based PINN 1.3.2.4. Generative Adversarial Based PINN 1.3.3. Operator Learning 1.3.4. Deep Learning-Traditional Algorithm Fusion 1.4. Constitutions of the Book Bibliography 2. Application of U-Net in 3D Steady Heat Conduction Solver 2.1. Traditional Methods 2.1.1. Analytical Methods 2.1.2. Numerical Methods 2.2. Literature Review 2.3. 3D Heat Conduction Solvers via Deep Learning 2.3.1. Heat Conduction Model 2.3.2. Data Set 2.3.2.1. Thermophysical Parameters 2.3.2.2. Basic Dataset 2.3.2.3. Open-Source Dataset 2.3.2.4. Enhanced Dataset 2.3.3. Architecture of the Network 2.3.4. Loss Functions 2.3.5. Pre-Experiments 2.3.5.1. Activation Function 2.3.5.2. Learning Rate 2.3.5.3. Dropout Ratio 2.3.5.4. Split Ratio 2.3.5.5. Optimizer 2.3.6. Results 2.3.6.1. Passive Cases 2.3.6.2. Active Cases 2.3.6.3. Computing Acceleration 2.4. Conclusion Bibliography 3. Inversion of Complex Surface Heat Flux Based on ConvLSTM 3.1. Introduction 3.2. Progress in Inversion Research 3.2.1. Conventional Approach 3.2.2. Artificial Neural Network 3.3. Methods 3.3.1. Physical Model of Heat Conduction 3.3.2. 3D Transient Forward Solver Based on Joint Simulation 3.3.3. Neural Network Framework Based on ConvLSTM 3.3.3.1. Fully Connected Network 3.3.3.2. Recurrent Neural Network 3.3.3.3. Convolutional LSTM 3.4. Results and Discussion 3.4.1. Training of the ConvLSTM 3.4.2. Inversion of the Regular Plane 3.4.3. Inversion of the Complex Surface 3.4.3.1. Thermal Inversion Results of the Fixed Complicated Model 3.4.3.2. Thermal Inversion Results of the Variable Complicated Model 3.4.4. Statistical Analysis and Comparison 3.4.5. Engineering Application 3.5. Conclusion Bibliography 4. Reconstruction of Thermophysical Parameters Based on Deep Learning 4.1. Introduction 4.1.1. Physical Foundation 4.2. Progress in Inversion Research 4.2.1. Gradient-Based Methods 4.2.1.1. LM Method 4.2.1.2. Conjugate Gradient Method 4.2.2. Global Optimization Algorithm 4.2.2.1. Genetic Algorithm 4.2.2.2. Particle Swarm Optimization 4.2.3. Deep Learning Approach 4.2.4. Structure of the Chapter 4.3. Physical Model and Data Generation 4.3.1. 2D Heat Conduction Model 4.3.2. 3D Heat Conduction Model 4.3.3. Data Generation 4.3.3.1. The Architecture of the PINN and Its Loss Functions 4.3.3.2. Comparison with Commercial Software 4.4. Denoising Process 4.4.1. Conventional Denoising Approach 4.4.2. Deep Learning Denoising Framework 4.4.3. Training and Testing 4.4.4. Comparisons with Other Approaches 4.5. Inversion Process 4.5.1. 2D Cases 4.5.1.1. DL Framework 4.5.1.2. Training and Testing 4.5.2. 3D Cases 4.5.2.1. DL Framework 4.5.2.2. Reconstructing Results 4.5.2.3. Statistics Analyze 4.5.2.4. Generalization Ability 4.5.2.5. Computational Speed 4.5.2.6. Comparisons with Conventional Network 4.6. Conclusion Bibliography 5 Advanced Deep Learning Techniques in Computational Physics 5.1. Physics Informed Neural Network 5.1.1. Fully Connected-Based PINN 5.1.1.1. Cylindrical Coordinate System 5.1.1.2. Spherical Coordinate System 5.1.1.3. Parabolic Coordinate System 5.1.2. Convolutional-Based PINN 5.2. Graph Neural Networks 5.2.1. Architecture of the GNN 5.2.2. Data Generation and Training 5.2.3. Results 5.3. Fourier Neural Networks 5.3.1. Methods 5.3.1.1. Framework Architecture 5.3.1.2. Physics Model 5.3.1.3. Data Generation 5.3.1.4. Training 5.3.2. Results and Discussion 5.3.2.1. Prediction Accuracy 5.3.2.2. Statistical Analysis 5.3.2.3. Comparison 5.4. Conclusion Bibliography Index