This book investigates in detail the emerging deep learning (DL) technique in computational physics, assessing its promising potential to substitute conventional numerical solvers for calculating the fields in real-time. After good training, the proposed architecture can resolve both the forward computing and the inverse retrieve problems.
Pursuing a holistic perspective, the book includes the following areas. The first chapter discusses the basic DL frameworks. Then, the steady heat conduction problem is solved by the classical U-net in Chapter 2, involving both the passive and active cases. Afterwards, the sophisticated heat flux on a curved surface is reconstructed by the presented Conv-LSTM, exhibiting high accuracy and efficiency. Additionally, a physics-informed DL structure along with a nonlinear mapping module are employed to obtain the space/temperature/time-related thermal conductivity via the transient temperature in Chapter 4. Finally, in Chapter 5, a series of the latest advanced frameworks and the corresponding physics applications are introduced.
As deep learning techniques are experiencing vigorous development in computational physics, more people desire related reading materials. This book is intended for graduate students, professional practitioners, and researchers who are interested in DL for computational physics.
Author(s): Yinpeng Wang, Qiang Ren
Publisher: CRC Press
Year: 2023
Language: English
Pages: 199
City: Boca Raton
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
