book

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

Name: Deep Learning-Based Forward Modeling and Inversion Techniques for Computational Physics Problems
ISBN: 9781000896671

by Yinpeng Wang, Qiang Ren

July 2023

Intermediate to advanced

194 pages

5h 26m

English

CRC Press

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Cover Page
Half-Title Page
Title Page
Copyright Page
Dedication Page
Contents
Preface
Symbols
1 Deep Learning Framework and Paradigm in Computational Physics
1.1 Traditional Numerical Algorithms1.1.1 Moment of Method1.1.2 Monte Carlo Method1.2 Basic Neural Network Structure1.2.1 Fully Connected Neural Network1.2.2 Convolutional Neural Network1.2.3 Recurrent Neural Network1.2.4 Generative Adversarial Network1.3 Paradigms in Deep Learning1.3.1 Data Driven1.3.2 Physics Constraint1.3.2.1 Fully Connected Based PINN1.3.2.2 Convolutional Based PINN1.3.2.3 Recurrent Based PINN1.3.2.4 Generative Adversarial Based PINN1.3.3 Operator Learning1.3.4 Deep Learning-Traditional Algorithm Fusion1.4 Constitutions of the BookBibliography
2 Application of U-Net in 3D Steady Heat Conduction Solver
2.1 Traditional Methods2.1.1 Analytical Methods2.1.2 Numerical Methods2.2 Literature Review2.3 3D Heat Conduction Solvers via Deep Learning2.3.1 Heat Conduction Model2.3.2 Data Set2.3.2.1 Thermophysical Parameters2.3.2.2 Basic Dataset2.3.2.3 Open-Source Dataset2.3.2.4 Enhanced Dataset2.3.3 Architecture of the Network2.3.4 Loss Functions2.3.5 Pre-Experiments2.3.5.1 Activation Function2.3.5.2 Learning Rate2.3.5.3 Dropout Ratio2.3.5.4 Split Ratio2.3.5.5 Optimizer2.3.6 Results2.3.6.1 Passive Cases2.3.6.2 Active Cases2.3.6.3 Computing Acceleration2.4 ConclusionBibliography

3 Inversion of Complex Surface Heat Flux Based on ConvLSTM
3.1 Introduction3.2 Progress in Inversion Research3.2.1 Conventional Approach3.2.2 Artificial Neural Network3.3 Methods3.3.1 Physical Model of Heat Conduction3.3.2 3D Transient Forward Solver Based on Joint Simulation3.3.3 Neural Network Framework Based on ConvLSTM3.3.3.1 Fully Connected Network3.3.3.2 Recurrent Neural Network3.3.3.3 Convolutional LSTM3.4 Results and Discussion3.4.1 Training of the ConvLSTM3.4.2 Inversion of the Regular Plane3.4.3 Inversion of the Complex Surface3.4.3.1 Thermal Inversion Results of the Fixed Complicated Model3.4.3.2 Thermal Inversion Results of the Variable Complicated Model3.4.4 Statistical Analysis and Comparison3.4.5 Engineering Application3.5 ConclusionBibliography
4 Reconstruction of Thermophysical Parameters Based on Deep Learning
4.1 Introduction4.1.1 Physical Foundation4.2 Progress in Inversion Research4.2.1 Gradient-Based Methods4.2.1.1 LM Method4.2.1.2 Conjugate Gradient Method4.2.2 Global Optimization Algorithm4.2.2.1 Genetic Algorithm4.2.2.2 Particle Swarm Optimization4.2.3 Deep Learning Approach4.2.4 Structure of the Chapter4.3 Physical Model and Data Generation4.3.1 2D Heat Conduction Model4.3.2 3D Heat Conduction Model4.3.3 Data Generation4.3.3.1 The Architecture of the PINN and Its Loss Functions4.3.3.2 Comparison with Commercial Software4.4 Denoising Process4.4.1 Conventional Denoising Approach4.4.2 Deep Learning Denoising Framework4.4.3 Training and Testing4.4.4 Comparisons with Other Approaches4.5 Inversion Process4.5.1 2D Cases4.5.1.1 DL Framework4.5.1.2 Training and Testing4.5.2 3D Cases4.5.2.1 DL Framework4.5.2.2 Reconstructing Results4.5.2.3 Statistics Analyze4.5.2.4 Generalization Ability4.5.2.5 Computational Speed4.5.2.6 Comparisons with Conventional Network4.6 ConclusionBibliography
5 Advanced Deep Learning Techniques in Computational Physics
5.1 Physics Informed Neural Network5.1.1 Fully Connected-Based PINN5.1.1.1 Cylindrical Coordinate System5.1.1.2 Spherical Coordinate System5.1.1.3 Parabolic Coordinate System5.1.2 Convolutional-Based PINN5.2 Graph Neural Networks5.2.1 Architecture of the GNN5.2.2 Data Generation and Training5.2.3 Results5.3 Fourier Neural Networks5.3.1 Methods5.3.1.1 Framework Architecture5.3.1.2 Physics Model5.3.1.3 Data Generation5.3.1.4 Training5.3.2 Results and Discussion5.3.2.1 Prediction Accuracy5.3.2.2 Statistical Analysis5.3.2.3 Comparison5.4 ConclusionBibliography
Index

Overview

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.

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