Machine Learning Techniques for Space Weather

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
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