Analysis and Visualization of Discrete Data Using Neural Networks

✍ Scribed by Koji Koyamada

• Publisher: World Scientific Publishing Company
• Year: 2024
• Tongue: English
• Leaves: 230
• Category: Library

✦ Synopsis

This book serves as a comprehensive step-by-step guide on data analysis and statistical analysis. It covers fundamental operations in Excel, such as table components, formula bar, and ribbon, and introduces visualization techniques and PDE derivation using Excel. It also provides an overview of Google Colab, including code and text cells, and explores visualization and deep learning applications.Key features of the book include topics like statistical analysis, regression analysis, optimization, correlation analysis, and neural networks. It adopts a practical approach by providing examples and step-by-step instructions for learners to apply the techniques to real-world problems.The book also highlights the strengths and features of both Excel and Google Colab, allowing learners to leverage the capabilities of each platform. The clear explanations of concepts, visual aids, and code snippets aid comprehension help learners understand the principles of data analysis and statistical analysis. Overall, this book serves as a valuable resource for professionals, researchers, and students seeking to develop skills in data analysis, regression statistics, optimization, and advanced modeling techniques using Excel, Colab, and neural networks.

✦ Table of Contents

Contents
1. Introduction
1.1. Basic operations of Excel
1.1.1. Table components
1.1.2. Name box and formula bar
1.1.3. Ribbon
1.1.4. File tab and Backstage view
1.1.5. Autofill
1.1.6. Relative reference
1.1.7. Absolute reference
1.1.8. Introduction of visualization with Excel
1.1.9. Introduction of PDE derivation with Excel
1.2. Basic operations of Google Colab (Colab)
1.2.1. Code cell
1.2.2. Text cell
1.2.3. Introduction to visualization with Colab
1.2.4. Introduction of deep learning with Colab
1.3. Organization of this document
2. Basic
2.1. Background
2.1.1. Data analysis using NNs
2.1.2. Format of physical data
2.1.3. Physical data visualization
2.1.3.1. 1-D plot
2.1.3.2. 2-D Plot
2.1.3.3. 3-D Plot
2.1.3.4. Particle-based volume rendering
2.2. Statistical Analysis in Excel
2.2.1. Correlation analysis
2.2.2. F-test
2.2.3. t-Test
2.2.4. Z-test
2.3. Regression analysis
2.3.1. Model characteristics
2.3.2. Regression analysis assumptions
2.3.2.1. Visualization of normal probability plots
2.3.2.2. Breusch–Pagan test
2.3.3. Regression analysis using the data analysis tools in Excel
2.3.3.1. Variable reduction method
2.3.3.2. Autoregression
2.3.4. Excel macro
2.3.5. Implementation of the variable reduction method using Excel VBA
2.4. What-if analysis
2.5. Solver
2.5.1. Optimization
2.5.2. Implementation of regression analysis
2.6. Colab
2.6.1. Correlation analysis
2.6.2. F-test
2.6.3. t-Test
2.6.4. Z-test
2.6.5. Regression analysis
2.6.6. Optimization problem
2.7. NNs
2.7.1. Universal approximation theorem
2.7.2. Regression analysis using NNs
2.7.3. NN implementation using Excel VBA
2.7.4. Function approximation using NNs
2.7.5. Point cloud data analysis using NNs: Application example
2.7.6. Line group data analysis using NN application examples
3. Practical Part
3.1. About PINNs
3.2. Automatic differentiation in NN
3.3. Using automatic differentiation in regression equation
3.4. Automatic differentiation using Colab
3.5. Increasing the accuracy of visualization of magnetic line group data using automatic differentiation
3.6. Generation of a CAD model from point cloud data using point cloud data processing software
4. Advanced Application Section
4.1. Derivation of PDEs describing physical data
4.1.1. Related research
4.1.2. PDE derivation using regularized regression analysis
4.1.3. Definition of error
4.1.4. Example of PDE derivation
4.1.4.1. One-dimensional advection–diffusion equation
4.1.4.2. One-dimensional KdV equation
4.1.4.3. One-dimensional Burgers’ equation
4.1.4.4. One-dimensional Poisson’s equation
4.1.4.5. One-dimensional heat conduction equation
4.1.4.6. One-dimensional wave equation
4.1.4.7. Two-dimensional linear stress analysis
4.1.4.8. Three-dimensional advection–diffusion equation
4.2. Use of visual analysis techniques
4.3. Methods for solving a given PDE
4.3.1. How to solve PDEs using the Fourier transform
4.3.2. PDE approximate solution
4.3.2.1. Finite element method (FEM)
4.3.2.2. Finite difference method (FDM)
4.3.3. How to find solutions to PDEs using PINNs
4.3.3.1. Constructing a model using NNs
4.3.3.2. Computation of PDE residuals
4.3.4. Example of finding solutions to PDEs using PINNs
4.3.4.1. One-dimensional advection–diffusion equation
4.3.4.2. One-dimensional Burgers’ equation
4.3.4.3. One-dimensional KdV equation
4.3.4.4. One-dimensional Poisson’s equation
4.3.4.5. One-dimensional heat conduction problem
4.3.4.6. One-dimensional wave equation
4.3.4.7. Two-dimensional linear stress analysis
4.3.4.8. Three-dimensional advection–diffusion equation
4.3.5. Implementation of the PDE solution method
4.3.5.1. Implementation using Colab
4.3.5.2. Implementation using FEMAP
5. Physically Based Surrogate Model
5.1. About the CAE surrogate model
5.1.1. Example of SM construction
5.1.1.1. Case 1: Heat management of laptop computers
5.1.1.2. Case 2: Heat management at the switched reluctance motor (SRM)
5.1.1.3. Use of Excel in SM construction
5.1.2. Expectations for physics-based learning
5.2. Application to carbon neutrality (CN)
6. Closing Remarks
References
Index