Artificial Intelligence for Scientific Discoveries: Extracting Physical Concepts from Experimental Data Using Deep Learning

Preface
Acknowledgements
Contents
1 Introduction
	1.1 Motivation
	1.2 Physicist's Discovery Process
	1.3 Extracting Relevant Parameters from Experimental Data
	1.4 Outline
Part I Machine Learning Background
2 Machine Learning in a Nutshell
	2.1 Supervised Learning
	2.2 Unsupervised Learning
	2.3 Reinforcement Learning
	2.4 Bias-Variance Tradeoff
3 Artificial Neural Networks
	3.1 Single Artificial Neuron
	3.2 Activation Functions
	3.3 Neural Networks
	3.4 Universality Theorem
	3.5 Training of Neural Networks
		3.5.1 Stochastic Gradient Descent
		3.5.2 Convergence and Choice of Hyperparameters
		3.5.3 Generalization
	3.6 Deep Learning
4 Autoencoders
Part II Overview of Using Machine Learning for Scientific Discoveries
5 Creating Experimental Setups
	5.1 Problem Setting from Quantum Optics
		5.1.1 Entanglement of Bipartite Systems
		5.1.2 Entanglement of Multipartite Systems
		5.1.3 Preparation of Photon States
	5.2 Creating Experimental Setups Using Projective Simulation
		5.2.1 Architecture for PS Agent
		5.2.2 Training of the PS Agent
		5.2.3 Results
	5.3 Conceptual Insights from Action Composition
6 Model Creation
	6.1 Optimizing Model Parameters
	6.2 Discovering Physical Laws
		6.2.1 Symbolic Regression
		6.2.2 Extracting Physical Laws from Data
7 Model Testing
	7.1 Statistical Setting
	7.2 Approximation of Probability Density Functions
		7.2.1 Parametric Modelling
		7.2.2 Non-parametric Modelling
	7.3 Statistical Hypothesis Testing
	7.4 Identifying the Discrepant Regions
	7.5 Application for Model Testing
Part III Representation Learning for Physical Discoveries
8 Theory: Formalizing the Process of Human Model Building
	8.1 Motivation
	8.2 Physicist's Reasoning Process
	8.3 Experimental Setting and Data Creation
	8.4 Criteria for Operationally Meaningful Representations
		8.4.1 Minimal Representation
		8.4.2 Separation of Physical Parameters
		8.4.3 Simple Update Rules
	8.5 Criteria for Mathematically Meaningful Representations
		8.5.1 Koopman Operator Theory
		8.5.2 Representation of Koopman Eigenfunctions
	8.6 Criteria for Physically Meaningful Representations
		8.6.1 Interaction Graph
		8.6.2 Representation of Interaction Graph
9 Methods: Using Neural Networks to Find Simple Representations
	9.1 Motivation
	9.2 General Network Structure to Learn Representations
	9.3 Network Structures for Separating Parameters
		9.3.1 Statistically Independent
		9.3.2 Operationally Meaningful
	9.4 Network Structure to Find Representations with Simple Update Rules
	9.5 Optimality Guarantees on the Representation
	9.6 Network Structure to Find Koopman Eigenfunctions
	9.7 Network Structure to Find Interaction Graphs
		9.7.1 Graph Neural Networks
		9.7.2 Network Structure to Learn Interaction Graphs
10 Applications: Physical Toy Examples
	10.1 Motivation
	10.2 Damped Pendulum
	10.3 Dynamics of the Nonlinear Pendulum
	10.4 Conservation of Angular Momentum
	10.5 Representation of Qubits
		10.5.1 Minimal Representations for Pure Quantum States
		10.5.2 Local Representation of Two-Qubit States
	10.6 Charged Particles
		10.6.1 Single Encoder
		10.6.2 Multiple Encoders
	10.7 Heliocentric Solar System
	10.8 Several Particles Connected by Springs
11 Future Research Directions and Further Reading
	11.1 Finding Measurement Strategies and Representations
	11.2 Interpretability and Generalization of SciNet
Part IV Future Prospects
12 Future Prospects
	12.1 AI Physicist
	12.2 Learning Procedures Instead of Simple Functions
	12.3 AI for Foundations of Physics
Appendix A Interpretation of the Number of Latent Variables
Appendix B Variational Autoencoders
Appendix C Implementation Details
Appendix D Representations of Cyclic Parameters
Appendix E Classical Mechanics Derivation for Charged Masse
Appendix  References