Machine Learning Techniques for Space Weather

Description

Machine Learning Techniques for Space Weather provides a thorough and accessible presentation of machine learning techniques that can be employed by space weather professionals. Additionally, it presents an overview of real-world applications in space science to the machine learning community, offering a bridge between the fields. As this volume demonstrates, real advances in space weather can be gained using nontraditional approaches that take into account nonlinear and complex dynamics, including information theory, nonlinear auto-regression models, neural networks and clustering algorithms. Offering practical techniques for translating the huge amount of information hidden in data into useful knowledge that allows for better prediction, this book is a unique and important resource for space physicists, space weather professionals and computer scientists in related fields. Front Matter Copyright Contributors Introduction Acknowledgments References Societal and Economic Importance of Space Weather What is Space Weather? Why Now? Impacts Geomagnetically Induced Currents Global Navigation Satellite Systems Single-Event Effects Other Radio Systems Satellite Drag Looking to the Future Summary and Conclusions Acknowledgments References Data Availability and Forecast Products for Space Weather Introduction Data and Models Based on Machine Learning Approaches Space Weather Agencies Government Agencies NOAA's Data and Products NASA European Space Agency The US Air Force Weather Wing Academic Institutions Kyoto University, Japan Rice University, USA Laboratory for Atmospheric and Space Physics, USA Commercial Providers Other Nonprofit, Corporate Research Agencies USGS JHU Applied Physics Lab US Naval Research Lab Other International Service Providers Summary References An Information-Theoretical Approach to Space Weather Introduction Complex Systems Framework State Variables Dependency, Correlations, and Information Mutual Information as a Measure of Nonlinear Dependence Cumulant-Based Cost as a Measure of Nonlinear Dependence Causal Dependence Transfer Entropy and Redundancy as Measures of Causal Relations Conditional Redundancy Significance of Discriminating Statistics Mutual Information and Information Flow Examples From Magnetospheric Dynamics Significance as an Indicator of Changes in Underlying Dynamics Detecting Dynamics in a Noisy System Cumulant-Based Information Flow Discussion Summary Acknowledgments References Regression What is Regression? Learning From Noisy Data Prediction Errors A Probabilistic Set-Up The Least Squares Method for Linear Regression The Least Squares Method and the Best Linear Predictor The Least Squares Method and the Maximum Likelihood Principle A More General Approach and Higher-Order Predictors Overfitting The Order Selection Problem Error Decomposition: The Bias Versus Variance Trade-Off Some Popular Order Selection Criteria Regularization From Point Predictors to Interval Predictors Distribution-Free Interval Predictors Probability Density Estimation Predictions Without Probabilities Approximation Theory Dense Sets Best Approximator Neural Networks The Backpropagation Algorithm: High-Level Idea Multiple Layers Networks (Deep Networks) Probabilities Everywhere: Bayesian Regression Gaussian Process Regression Learning in the Presence of Time: Identification of Dynamical Systems Linear Time-Invariant Systems Nonlinear Systems References Supervised Classification: Quite a Brief Overview Introduction Learning, Not Modeling An Outline Classifiers Preliminaries The Bayes Classifier Generative Probabilistic Classifiers Discriminative Probabilistic Classifiers Losses and Hypothesis Spaces 0–1 Loss Convex Surrogate Losses Particular Surrogate Losses Neural Networks Neighbors, Trees, Ensembles, and All that k Nearest Neighbors Decision Trees Multiple Classifier Systems Representations and Classifier Complexity Feature Transformations The Kernel Trick Dissimilarity Representation Feature Curves and the Curse of Dimensionality Feature Extraction and Selection Evaluation Apparent Error and Holdout Set Resampling Techniques Leave-One-Out and k-Fold Cross-Validation Bootstrap Estimators Tests of Significance Learning Curves and the Single Best Classifier Some Words About More Realistic Scenarios Regularization Variations on Standard Classification Multiple Instance Learning One-Class Classification, Outliers, and Reject Options Contextual Classification Missing Data and Semisupervised Learning Transfer Learning and Domain Adaptation Active Learning Acknowledgments References Untangling the Solar Wind Drivers of the Radiation Belt: An Information Theoretical Approach Introduction Data Set Mutual Information, Conditional Mutual Information, and Transfer Entropy Applying Information Theory to Radiation Belt MeV Electron Data Radiation Belt MeV Electron Flux Versus Vsw Radiation Belt MeV Electron Flux Versus nsw Anticorrelation of Vsw and nsw and Its Effect on Radiation Belt Ranking of Solar Wind Parameters Based on Information Transfer to Radiation Belt Electrons Detecting Changes in the System Dynamics Discussion Geo-Effectiveness of Solar Wind Velocity nsw and Vsw Anticorrelation Geo-Effectiveness of Solar Wind Density Revisiting the Triangle Distribution Improving Models With Information Theory Selecting Input Parameters Detecting Nonstationarity in System Dynamics Prediction Horizon Summary Acknowledgments References Emergence of Dynamical Complexity in the Earth's Magnetosphere Introduction On Complexity and Dynamical Complexity Coherence and Intermittent Features in Time Series Geomagnetic Indices Scale-Invariance and Self-Similarity in Geomagnetic Indices Near-Criticality Dynamics Multifractional Features and Dynamical Phase Transitions Summary Acknowledgments References Applications of NARMAX in Space Weather Introduction NARMAX Methodology Forward Regression Orthogonal Least Square The Noise Model Model Validation Summary NARMAX and Space Weather Forecasting Geomagnetic Indices SISO Dst Index Continuous Time Dst model MISO Dst Kp Index Radiation Belt Electron Fluxes GOES High Energy SNB3GEO Comparison With NOAA REFM GOES Low Energy Summary of NARMAX Models NARMAX and Insight Into the Physics NARMAX Deduced Solar Wind-Magnetosphere Coupling Function Identification of Radiation Belt Control Parameters Solar Wind Density Relationship With Relativistic Electrons at GEO Geostationary Local Quasilinear Diffusion vs. Radial Diffusion Frequency Domain Analysis of the Dst Index Discussions and Conclusion References Probabilistic Forecasting of Geomagnetic Indices Using Gaussian Process Models Geomagnetic Time Series and Forecasting Dst Forecasting Models and Algorithms Probabilistic Forecasting Gaussian Processes Gaussian Process Regression: Formulation Gaussian Process Regression: Inference One-Hour Ahead Dst Prediction Data Source: OMNI Gaussian Process Dst Model Gaussian Process Auto-Regressive (GP-AR) GP-AR With eXogenous Inputs (GP-ARX) One-Hour Ahead Dst Prediction: Model Design Choice of Mean Function Choice of Kernel Model Selection: Hyperparameters Grid Search Coupled Simulated Annealing Maximum Likelihood Model Selection: Auto-Regressive Order GP-AR and GP-ARX: Workflow Summary Practical Issues: Software Experiments and Results Model Selection and Validation Performance Comparison of Hyperparameter Selection Algorithms Final Evaluation Sample Predictions With Error Bars Conclusion References Prediction of MeV Electron Fluxes and Forecast Verification Relativistic Electrons in Earth's Outer Radiation Belt Source, Loss, Transport, and Acceleration, Variation Numerical Techniques in Radiation Belt Forecasting Relativistic Electron Forecasting and Verification Forecast Verification Relativistic Electron Forecasting Summary References Artificial Neural Networks for Determining Magnetospheric Conditions Introduction A Brief Review of ANNs Methodology and Application The DEN2D Model Advanced Applications The DEN3D Model The Chorus and Hiss Wave Models Radiation Belt Flux Modeling Summary and Discussion Acknowledgments References Reconstruction of Plasma Electron Density From Satellite Measurements Via Artificial Neural Networks Overview Space Weather-Related Aspects and Motivation Plasma Density and the Plasmasphere Determining the Electron Density From Upper-Hybrid Band Resonance Frequency Brief Background on Neural Networks Basic Concepts Related to Neural Networks Neural Network Design Flow Importance of Validation Implementation of the Algorithm Training Data Set Input Data Output Data Neural Network Architecture Steps of the Design Flow Postprocessing Step Results Comparison With AURA and NURD Performance Comparison With Empirical Model of sheeley2001empirical Discussion and Future Directions Conclusions Acknowledgments References Classification of Magnetospheric Particle Distributions Via Neural Networks Introduction A Brief Introduction to the Earth's Magnetosphere Pitch Angle Distributions in the Magnetosphere Neural Networks Applied to Magnetospheric Particle Distribution Classification Basic Concepts and Applications of Neural Networks Self-Organizing Map Mathematical Background for the SOM's Learning Algorithm Implementation Geometrical Interpretation of the SOM's Learning Algorithm PAD Classification of Relativistic and Subrelativistic Electrons in the Van Allen Radiation Belts Step 1: Data Choice for the SOM's Training Phase Step 2: Preparing the Data to Use It as Input to the SOM Step 3: Determining the Classes Outputted by the SOM Step 4: Displaying Clustered Particle PAD Shapes as a Function of Radial Distance and Time Summary Acknowledgments References Machine Learning for Flare Forecasting The Solar Flare Prediction Problem Standard Machine Learning Methods Advanced Machine Learning Methods Innovative Machine Learning Methods The Technological Aspect Conclusions References Coronal Holes Detection Using Supervised Classification Introduction Data Preparation Coronal Hole Feature Extraction The SPoCA-Suite Modified SPoCA-CH Module Labeled Datasets Proposed Attributes Location Shape Measures Magnetic Flux Imbalance First- and Second-Order Statistics Sets of Attributes Used for Classification Supervised Classification Supervised Classification Algorithms Imbalanced Dataset Cost-Sensitive Learning Sampling Methods Ensemble Learning Training and Evaluation Protocol Training Hyperparameter Optimization During Training Evaluation Performance Metrics Results Cost-Sensitive Learning Versus Sampling Techniques Ensemble Learning Importance of Attributes Discussion and Conclusion Acknowledgments First-Order Image Statistics Second-Order Image Statistics Cooccurrence Matrix Notations Textural Features Classifier Hyperparameter Range Base Classifiers Ensemble Methods Relevance of Attributes References Solar Wind Classification Via k-Means Clustering Algorithm Introduction Basic Assumptions and Methodology k-Means Comparing 2-Means Clustering to Existing Solar Wind Categorization Schemes Model Selection, or How to Choose k Interpreting Clustering Results Using k-Means for Feature Selection Summary and Conclusion References Index A B C D E F G H I J K L M N O P Q R S T U V W Z