Mechanistic Data Science for STEM Education and Applications

✍ Scribed by Wing Kam Liu, Zhengtao Gan, Mark Fleming

• Publisher: Springer
• Year: 2021
• Tongue: English
• Leaves: 287
• Category: Library

✦ Synopsis

This book introduces Mechanistic Data Science (MDS) as a structured methodology for combining data science tools with mathematical scientific principles (i.e., “mechanistic” principles) to solve intractable problems. Traditional data science methodologies require copious quantities of data to show a reliable pattern, but the amount of required data can be greatly reduced by considering the mathematical science principles. MDS is presented here in six easy-to-follow modules: 1) Multimodal data generation and collection, 2) extraction of mechanistic features, 3) knowledge-driven dimension reduction, 4) reduced order surrogate models, 5) deep learning for regression and classification, and 6) system and design. These data science and mechanistic analysis steps are presented in an intuitive manner that emphasizes practical concepts for solving engineering problems as well as real-life problems. This book is written in a spectral style and is ideal as an entry leveltextbook for engineering and data science undergraduate and graduate students, practicing scientists and engineers, as well as STEM(Science, Technology, Engineering, Mathematics)high school students and teachers.

✦ Table of Contents

Preface
Acknowledgments
Contents
Chapter 1: Introduction to Mechanistic Data Science
1.1 A Brief History of Science: From Reason to Empiricism to Mechanistic Principles and Data Science
1.2 Galileo´s Study of Falling Objects
1.3 Newton´s Laws of Motion
1.4 Science, Technology, Engineering and Mathematics (STEM)
1.5 Data Science Revolution
1.6 Data Science for Fatigue Fracture Analysis
1.7 Data Science for Materials Design: What´s in the Cake Mix´´ 1.8 From Everyday Applications to Materials Design 1.8.1 Example: Tire Tread Material Design Using the MDS Framework 1.8.2 Gold and Gold Alloys for Wedding Cakes and Wedding Rings 1.9 Twenty-First Century Data Science 1.9.1 AlphaGo 1.9.2 3D Printing: From Gold Jewelry to Customized Implants 1.10 Outline of Mechanistic Data Science Methodology 1.11 Examples Describing the Three Types of MDS Problems 1.11.1 Determining Price of a Diamond Based on Features (Pure Data Science: Type 1) 1.11.2 Sports Analytics 1.11.2.1 Example:Moneyball´´: Data Science for Optimizing a Baseball Team Roster
1.11.3 Predicting Patient-Specific Scoliosis Curvature (Mixed Data Science and Surrogate: Type 2)
1.11.4 Identifying Important Dimensions and Damping in a Mass-Spring System (Type 3 Problem)
References
Chapter 2: Multimodal Data Generation and Collection
2.1 Data as the Central Piece for Science
2.2 Data Formats and Sources
2.3 Data Science Datasets
2.4 Example: Diamond Data for Feature-Based Pricing
2.5 Example: Data Collection from Indentation Testing
2.6 Summary of Multimodal Data Generation and Collection
References
Chapter 3: Optimization and Regression
3.1 Least Squares Optimization
3.1.1 Optimization
3.1.2 Linear Regression
3.1.3 Method of Least Squares Optimization for Linear Regression
3.1.4 Coefficient of Determination (r2) to Describe Goodness of Fit
3.1.5 Multidimensional Derivatives: Computing Gradients to Find Slope or Rate of Change
3.1.6 Gradient Descent (Advanced Topic: Necessary for Data Science)
3.1.7 Example: Moneyball´´: Data Science for Optimizing a Baseball Team Roster 3.1.7.1 Moneyball Regression Analysis Steps Step 1: Multimodal Data Generation and Collection Step 2: Feature Engineering Step 3: Dimension Reduction Step 4: Reduced Order Modeling Step 5: Regression and Classification Module 6: System and Design 3.1.8 Example: Indentation for Material Hardness and Strength 3.1.9 Example: Vickers Hardness for Metallic Glasses and Ceramics 3.2 Nonlinear Regression 3.2.1 Piecewise Linear Regression 3.2.2 Moving Average 3.2.3 Moving Least Squares (MLS) Regression 3.2.4 Example: Bacteria Growth 3.3 Regularization and Cross-Validation (Advanced Topic) 3.3.1 Review of the Lp-Norm 3.3.2 L1-Norm Regularized Regression 3.3.3 L2-Norm Regularized Regression 3.3.4 K-Fold Cross-Validation 3.4 Equations for Moving Least Squares (MLS) Approximation (Advanced Topic) References Chapter 4: Extraction of Mechanistic Features 4.1 Introduction 4.2 What Is aFeature´´
4.3 Normalization of Feature Data
4.3.1 Example: Home Buying
4.4 Feature Engineering
4.4.1 Example: Determining a New Store Location Using Coordinate Transformation Techniques
4.5 Projection of Images (3D to 2D) and Image Processing
4.6 Review of 3D Vector Geometry
4.7 Problem Definition and Solution
4.8 Equation of Line in 3D and the Least Square Method
4.8.1 Numerical Example
4.9 Applications: Medical Imaging
4.9.1 X-ray (Radiography)
4.9.2 Computed Tomography (CT)
4.9.3 Magnetic Resonance Imaging (MRI)
4.9.4 Image Segmentation
4.10 Extracting Geometry Features Using 2D X-ray Images
4.10.1 Coordinate Systems
4.10.2 Input Data
4.10.3 Vertebra Regions [Advanced Topic]
4.10.4 Calculating the Angle Between Two Vectors
4.10.5 Feature Definitions: Global Angles
4.11 Signals and Signal Processing Using Fourier Transform and Short Term Fourier Transforms
4.12 Fourier Transform (FT)
4.12.1 Example: Analysis of Separate and Combined Signals
4.12.2 Example: Analysis of Sound Waves from a Piano
4.13 Short Time Fourier Transform (STFT)
References
Chapter 5: Knowledge-Driven Dimension Reduction and Reduced Order Surrogate Models
5.1 Introduction
5.2 Dimension Reduction by Clustering
5.2.1 Clustering in Real Life: Jogging
5.2.2 Clustering for Diamond Price: From Jenks Natural Breaks to K-Means Clustering
5.2.3 K-Means Clustering for High-Dimensional Data
5.2.3.1 Example: Clustering of Diamonds Based on Multiple Features
5.2.4 Determining the Number of Clusters
5.2.5 Limitations of K-Means Clustering
5.2.6 Self-Organizing Map (SOM) [Advanced Topic]
5.2.6.1 An Engineering Example: Data-Driven Design for Additive Manufacturing Using SOM
5.3 Reduced Order Surrogate Models
5.3.1 A First Look at Principal Component Analysis (PCA)
5.3.2 Understanding PCA by Singular Value Decomposition (SVD) [Advanced Topic]
5.3.2.1 Recall Matrix Multiplication
5.3.2.2 Singular Value Decomposition
5.3.2.3 Matrix Order Reduction by SVD Truncation
5.3.2.4 Example: Spring-Mass Harmonic Oscillator
5.3.3 Further Understanding of Principal Component Analysis [Advanced Topic]
5.3.3.1 Variance and Covariance
5.3.3.2 Identifying Intrinsic Dimension of Spring-Mass System Using PCA/SVD
5.3.4 Proper Generalized Decomposition (PGD) [Advanced Topic]
5.3.4.1 From SVD to PGD
5.3.4.2 A Matrix Decomposition Example Using Incremental PGD
5.3.4.3 A PGD Example Using Modal Superposition
5.3.4.4 PGD for High-Dimensional Tensor Decomposition
5.4 Eigenvalues and Eigenvectors [Advanced Topic]
5.5 Mathematical Relation Between SVD and PCA [Advanced Topic]
References
Chapter 6: Deep Learning for Regression and Classification
6.1 Introduction
6.1.1 Artificial Neural Networks
6.1.2 A Brief History of Deep Learning and Neural Networks
6.2 Feed Forward Neural Network (FFNN)
6.2.1 A First Look at FFNN
6.2.2 General Notations for FFNN [Advanced Topic]
6.2.3 Apply FFNN to Diamond Price Regression
6.3 Convolutional Neural Network (CNN)
6.3.1 A First Look at CNN
6.3.2 Building Blocks in CNN
6.3.2.1 Convolution
6.3.2.2 Stride
6.3.2.3 Padding
6.3.2.4 Pooling
6.3.2.5 Fully Connected Networks
6.3.3 General Notations for CNN [Advanced Topic]
6.3.4 COVID-19 Detection from X-Ray Images of Patients [Advanced Topic]
6.4 Musical Instrument Sound Conversion Using Mechanistic Data Science
6.4.1 Problem Statement and Solutions
6.4.2 Mechanistic Data Science Model for Changing Instrumental Music [Advanced Topic]
6.5 Conclusion
References
Chapter 7: System and Design
7.1 Introduction
7.2 Piano to Guitar Musical Note Conversion (Type 3 General)
7.2.1 Mechanistic Data Science with a Spring Mass Damper System
7.2.2 Principal Component Analysis for Musical Note Conversion (Type 1 Advanced)
7.2.3 Data Preprocessing (Normalization and Scaling)
7.2.4 Compute the Eigenvalues and Eigenvectors for the Covariance Matrix of Bp and Bg
7.2.5 Build a Reduced-Order Model
7.2.6 Inverse Transform Magnitudes for all PCs to a Sound
7.2.7 Cumulative Energy for Each PC
7.2.8 Python Code for Step 1 and Step 2
7.2.9 Training a Fully-Connected FFNN
7.2.10 Code Explanation for Step 3
7.2.11 Generate a Single Guitar
7.2.12 Python Code for Step 4
7.2.13 Generate a Melody
7.2.14 Code Explanation for Step 5
7.2.15 Application for Forensic Engineering
7.3 Feature-Based Diamond Pricing (Type 1 General)
7.4 Additive Manufacturing (Type 1 Advanced)
7.5 Spine Growth Prediction (Type 2 Advanced)
7.6 Design of Polymer Matrix Composite Materials (Type 3 Advanced)
7.7 Indentation Analysis for Materials Property Prediction (Type 2 Advanced)
7.8 Early Warning of Rainfall Induced Landslides (Type 3 Advanced)
7.9 Potential Projects Using MDS
7.9.1 Next Generation Tire Materials Design
7.9.2 Antimicrobial Surface Design
7.9.3 Fault Detection Using Wavelet-CNN
References
Index