Physics of Data Science and Machine Learning

✍ Scribed by Ijaz A. Rauf

• Publisher: CRC Press
• Year: 2021
• Tongue: English
• Leaves: 211
• Edition: 1
• Category: Library

✦ Synopsis

Physics of Data Science and Machine Learning links fundamental concepts of physics to data science, machine learning and artificial intelligence for physicists looking to integrate these techniques into their work.

This book is written explicitly for physicists, marrying quantum and statistical mechanics with modern data mining, data science, and machine learning. It also explains how to integrate these techniques into the design of experiments, whilst exploring neural networks and machine learning building on fundamental concepts of statistical and quantum mechanics.

This book is a self-learning tool for physicists looking to learn how to utilize data science and machine learning in their research. It will also be of interest to computer scientists and applied mathematicians, alongside graduate students looking to understand the basic concepts and foundations of data science, machine learning, and artificial intelligence.

Although specifically written for physicists, it will also help provide non-physicists with an opportunity to understand the fundamental concepts from a physics perspective to aid the development of new and innovative machine learning and artificial intelligence tools.

Key features:

• Introduces the design of experiments and digital twin concepts in simple lay terms for physicists to understand, adopt, and adapt.
• Free from endless derivations, instead equations are presented and explained strategically and explain why it is imperative to use them and how they will help in the task at hand.
• Illustrations and simple explanations help readers visualize and absorb the difficult to understand concepts.

Ijaz A. Rauf is Adjunct Professor at the School of Graduate Studies, York University, Toronto, Canada. He is also an Associate Researcher at Ryerson University, Toronto, Canada and President of the Eminent-Tech Corporation, Bradford, ON, Canada.

✦ Table of Contents

Cover
Half Title
Title Page
Copyright Page
Dedication
Table of Contents
Preface: Motivation and Rationale
Author
CHAPTER 1 Introduction
1.1 A PHYSICIST’S VIEW OF THE NATURAL WORLD AND PROBABILITIES
1.2 DATA – TYPES OF DATA
1.2.1 Data to Information
1.2.2 Information to Knowledge
1.2.3 Critical Differences between Information and Knowledge
1.3 DATA MINING FOR KNOWLEDGE
1.4 MACHINE LEARNING AND ARTIFICIAL INTELLIGENCE
1.5 SCOPE: WHAT THIS TEXT COVERS
1.5.1 What This Text Does Not Cover
CHAPTER 2 An Overview of Classical Mechanics
2.1 NEWTONIAN MECHANICS
2.1.1 Newton’s Laws of Motion
2.1.2 Angular Momentum, Work, and Energy
2.1.3 Multiple Interactions and Center of Mass
2.1.4 The Law of Gravitation
2.2 LAGRANGIAN MECHANICS
2.2.1 Constraints
2.2.2 Degrees of Freedom and Generalized Coordinates
2.2.3 Virtual Work and Lagrange’s Equations
2.3 HAMILTONIAN MECHANICS
2.4 CLASSICAL FIELD THEORY
2.4.1 Nonrelativistic Field Theory
2.4.1.1 Gravitational Field
2.4.1.2 Charged Particle in an Electrical Field
2.4.1.3 Charged Particle in a Magnetic Field
2.4.1.4 Electrodynamics
2.4.2 Relativistic Field Theory
2.4.2.1 The Action Principle
2.4.2.2 Field Theory for Scalar Field
2.4.2.3 Generalization of Field Theory
2.5 MAXWELL AND BOLTZMANN EQUILIBRIUM STATISTICS
CHAPTER 3 An Overview of Quantum Mechanics
3.1 KINEMATICAL FRAMEWORK
3.1.1 Heisenberg’s Uncertainty Principle
3.1.2 Quantum Mechanical Operators
3.1.3 Quantum Mechanical Energy States
3.1.4 Quantum Confinement
3.2 DYNAMICS OF QUANTUM MECHANICAL SYSTEMS
3.2.1 Energy Eigenvalue for Harmonic Oscillator
3.2.2 Eigenfunction for the Harmonic Oscillator
3.2.3 Non-Eigen States
3.3 QUANTUM STATISTICAL MECHANICS
3.3.1 Expected Value and Standard Deviation
3.3.2 Quantum Statistics
3.4 QUANTUM FIELD THEORY
3.5 PERTURBATION THEORY
CHAPTER 4 Probabilistic Physics
4.1 PROBABILITY THEORY
4.1.1 Events and Sample Space
4.1.2 Expected Value
4.1.3 Probability Amplitude
4.1.4 Two-Slit Quantum Interference
4.2 PROBABILITY DISTRIBUTIONS
4.2.1 Binomial Distribution
4.2.2 Poisson Distribution
4.2.3 Normal Distribution
4.2.4 Uniform Distribution
4.2.5 Exponential Distribution
4.3 CENTRAL LIMIT THEOREM
4.3.1 Confidence Level and Interval
4.4 HYPOTHESIS TESTING
4.4.1 Types of Error in Hypothesis Testing
4.4.2 Types of Tests and Test Statistics
4.4.2.1 z-test
4.4.2.2 t-test
4.4.2.3 Test of Proportions
4.4.2.4 Test of k-Proportions or Test of Independence
4.4.2.5 Summary of Hypothesis Testing
CHAPTER 5 Design of Experiments and Analyses
5.1 MEASUREMENT SYSTEM ANALYSIS
5.1.1 Precision and Accuracy
5.1.2 Types of Errors
5.1.3 Error Estimation and Reporting
5.2 MULTIVARIATE REGRESSION ANALYSIS
5.3 ANALYSIS OF VARIANCE
5.4 EXPERIMENTAL DESIGNS
5.4.4 Historical Data Anal ysis
5.4.1 Two-Level Full Factorial Design and Analysis
5.4.2 Three-Level Full Factorial Design and Analysis
5.4.3 Partial Factorial or Fractional Factorial Designs
5.4.3.1 Half Fraction of 2k Design
5.4.3.2 Orthogonal Array Designs or Taguchi’s L Designs
5.5 SYSTEMS MODELING
5.5.1 Linear Models
5.5.2 Nonlinear Models
CHAPTER 6 Basics of Machine Learning
6.1 INFORMATION THEORY
6.1.1 Channel Speed Limit
6.1.2 Communication System Architecture
6.1.3 Digitalization of Information
6.1.4 Source Coding
6.1.5 Entropy and Information Content
6.2 DATA HANDLING
6.2.1 Supervised Learning
6.2.1.1 Classification
6.2.1.2 Regression
6.2.1.3 Time Series Prediction
6.2.2 Semisupervised Learning
6.2.3 Unsupervised Learning
6.2.3.1 Projection
6.2.3.2 Clustering
6.2.3.3 Density Estimation
6.2.3.4 Generative Models
6.3 LEARNING INPUT AND OUTPUT FUNCTIONS
6.3.1 Input Vectors
6.3.2 Output
6.4 BAYESIAN DECISION THEORY
6.4.1 Sampling Theory Approach
6.4.2 Bayesian Inference Approach
6.5 NEURAL NETWORKS
6.5.1 Multilayer Neural Networks
6.6 SUPPORT VECTOR MACHINES
6.7 THE KERNEL FUNCTION
CHAPTER 7 Prediction, Optimization, and New Knowledge Development
7.1 DIGITAL TWINS
7.1.1 Advantages of Digital Twins
7.1.2 Development of Digital Twins
7.2 MONTE CARLO SIMULATIONS
7.3 RESPONSE SURFACE METHODOLOGY
7.3.1 The Sequential Application of Response Surface Methodology
7.3.2 Robust Design
7.3.3 Simulation Tools for Response Surface Methodology
7.4 MODEL VERIFICATION AND VALIDATION
7.4.1 Various Model Validation Techniques
7.4.2 Automation Tools for Model Verification and
Validation
REFERENCES
INDEX