On Spatio-Temporal Data Modelling and Uncertainty Quantification Using Machine Learning and Information Theory (Springer Theses)

✍ Scribed by Fabian Guignard

• Publisher: Springer
• Year: 2022
• Tongue: English
• Leaves: 170
• Category: Library

✦ Synopsis

The gathering and storage of data indexed in space and time are experiencing unprecedented growth, demanding for advanced and adapted tools to analyse them. This thesis deals with the exploration and modelling of complex high-frequency and non-stationary spatio-temporal data. It proposes an efficient framework in modelling with machine learning algorithms spatio-temporal fields measured on irregular monitoring networks, accounting for high dimensional input space and large data sets. The uncertainty quantification is enabled by specifying this framework with the extreme learning machine, a particular type of artificial neural network for which analytical results, variance estimation and confidence intervals are developed. Particular attention is also paid to a highly versatile exploratory data analysis tool based on information theory, the Fisher-Shannon analysis, which can be used to assess the complexity of distributional properties of temporal, spatial and spatio-temporal data sets. Examples of the proposed methodologies are concentrated on data from environmental sciences, with an emphasis on wind speed modelling in complex mountainous terrain and the resulting renewable energy assessment. The contributions of this thesis can find a large number of applications in several research domains where exploration, understanding, clustering, interpolation and forecasting of complex phenomena are of utmost importance.

✦ Table of Contents

Supervisor’s Foreword
Acknowledgements
Contents
Abbreviations
1 Introduction
1.1 Sketch of the Thesis
1.2 Spatio-Temporal Data Modelling and Analysis
1.2.1 Statistical Interpolation for Spatio-Temporal Data
1.2.2 Machine Learning for Spatial Data
1.2.3 Uncertainty Quantification
1.2.4 Information Theory as an Advanced Exploratory Tool
1.3 Objectives
1.4 Contributions
1.5 Thesis Organisation
References
2 Study Area and Data Sets
2.1 Switzerland and Its Topography
2.2 MeteoSwiss Wind Speed Data
2.2.1 Data Wrangling, Cleaning and Missing Values
2.2.2 Exploratory Data Analysis
2.3 MoTUS High-Frequency Wind Speed Data
2.3.1 Data Wrangling, Cleaning and Missing Values
2.3.2 Exploratory Data Analysis
2.4 Summary
References
3 Advanced Exploratory Data Analysis
3.1 Empirical Orthogonal Functions
3.1.1 Spatial Formulation
3.1.2 Temporal Formulation
3.1.3 Singular Value Decomposition
3.2 Variography
3.3 Wavelet Variance Analysis
3.3.1 Multiresolution Wavelet Analysis
3.3.2 The Wavelet Variance
3.3.3 Application to the MoTUS Data
3.4 Summary
References
4 Fisher-Shannon Analysis
4.1 Related Work
4.2 Fisher-Shannon Analysis
4.2.1 Shannon Entropy Power and Fisher Information Measure
4.2.2 Properties
4.2.3 Fisher-Shannon Complexity
4.2.4 Fisher-Shannon Information Plane
4.3 Analytical Solutions for Some Distributions
4.3.1 Gamma Distribution
4.3.2 Weibull Distribution
4.3.3 Log-Normal Distribution
4.4 Data-Driven Non-parametric Estimation
4.5 Experiments and Case Studies
4.5.1 Logistic Map
4.5.2 Normal Mixtures Densities
4.5.3 MoTUS Data: Advanced EDA
4.5.4 MoTUS Data: Complexity Discrimination
4.5.5 Other Applications
4.6 Summary
References
5 Spatio-Temporal Prediction with Machine Learning
5.1 Motivation
5.2 Machine-Learning-Based Framework for Spatio-Temporal Interpolation
5.2.1 Decomposition of Spatio-Temporal Data Using EOFs
5.2.2 Spatial Modelling of the Coefficients
5.3 Simulated Data Case Study
5.4 Experiment on Temperature Monitoring Network
5.5 Experiment on the MeteoSwiss Data
5.6 Summary
References
6 Uncertainty Quantification with Extreme Learning Machine
6.1 Related Work and Motivation
6.2 Background and Notations
6.2.1 Extreme Learning Machine
6.2.2 Regularised ELM
6.2.3 ELM Ensemble
6.3 Analytical Developments
6.3.1 Bias and Variance for a Single ELM
6.3.2 Bias and Variance for ELM Ensemble
6.3.3 Use of Random Variable Quadratic Forms
6.3.4 Correlation Between Two ELMs
6.4 Variance Estimation of ELM Ensemble
6.4.1 Estimation of the Least-Squares Bias Variation
6.4.2 Estimation Under Independence and Homoskedastic Assumptions
6.4.3 Estimation Under Independence and Heteroskedastic Assumptions
6.5 Synthetic Experiments
6.5.1 One-Dimensional Case
6.5.2 Multi-dimensional Case
6.5.3 Towards Confidence Intervals
6.6 Summary
References
7 Spatio-Temporal Modelling Using Extreme Learning Machine
7.1 Spatio-Temporal ELM Model
7.1.1 ELM Modelling of the Spatial Coefficients
7.1.2 Model Variance Estimation
7.1.3 Prediction Variance Estimation
7.2 Application to the MeteoSwiss Data
7.2.1 Wind Speed Modelling
7.2.2 Residual Analysis
7.3 Aeolian Energy Potential Estimation
7.3.1 Wind Speed Conversion and Uncertainty Propagation
7.3.2 Power Estimation for Switzerland
7.4 Summary
References
8 Conclusions, Perspectives and Recommendations
8.1 Fisher-Shannon Analysis and Complexity Quantification
8.1.1 Thesis Achievements
8.1.2 Implications and Future Challenges
8.2 Spatio-Temporal Interpolation with Machine Learning
8.2.1 Thesis Achievements
8.2.2 Implications and Future Challenges
8.3 Uncertainty Quantification with Extreme Learning Machine
8.3.1 Thesis Achievements
8.3.2 Implications and Future Challenges
8.4 Application on Wind Phenomenon and Wind Energy Potential Estimation
8.4.1 Thesis Achievements
8.4.2 Implications and Future Challenges
References