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

Description

Will research soon be done by artificial intelligence, thereby making human researchers superfluous? This book explains modern approaches to discovering physical concepts with machine learning and elucidates their strengths and limitations. The automation of the creation of experimental setups and physical models, as well as model testing are discussed. The focus of the book is the automation of an important step of the model creation, namely finding a minimal number of natural parameters that contain sufficient information to make predictions about the considered system. The basic idea of this approach is to employ a deep learning architecture, SciNet, to model a simplified version of a physicist's reasoning process. SciNet finds the relevant physical parameters, like the mass of a particle, from experimental data and makes predictions based on the parameters found. The author demonstrates how to extract conceptual information from such parameters, e.g., Copernicus' conclusion that the solar system is heliocentric.    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