This thesis deals with the exploration and modelling of complex high-frequency and non-stationary spatio-temporal data. Its main contributions are the following:
• Investigate the use of Information Theory (IT) measures to assess the complexity of distri­ butional properties of temporal, spatial and spatio-temporal data sets;
• Propose and elaborate an efficient fram ework in modelling with Machine Learning (ML) algorithms spatio-temporal fields measured on irr egular monitoring networks, accounting for high dimensional input space and large data sets, and enabling Uncertainty Quantification (UQ);
• Develop analytical results and estimates of variance and confidence intervals for Extreme Learning Machines (ELM) with comprehensive testing on simulated and real data sets.
These methodological contributions can find a large number of applications in several research domains where explora tion, underst anding , clust ering , interpolation and forecasting of complex spatio-temporal phenomena are of utmost importance. For instance, they are applied herein to study wind in Switzerland. Proper modelling of this turbulent and highly variable environmental phenomenon is indeed crucial for accurate renewable energy potential estimates, risk assessment and natural hazards.
Two data sets are studied throughout the manuscript to exemplify the methodological contribu­ tions. The first one consists of ten years of wind sp eed time series measurements at hourly frequency collected by MeteoSwiss at several hundreds of stations in Switzerland, which has a typical com­ plex mountainous terrain influencing spatially the spatio-temporal wind dynamic . Insights on the complex behaviour of t he wind phenomenon are also gained by studying a second data set of wind speed profile recorded at 20Hz along a mast set up in an urban zone for severa l months.
The first half of the manuscript concerns Exploratory Data Analysis (EDA). Par ticular attention is paid to a highly versatile EDA tool based on IT, involving Fisher information and Shannon entropy from which one can obtain a statistical complexity measure. Non-parametric estimates of those quantities enable numerous applications in the t ime series context from which various insights are extracted from data. The second half deals with spatio-temporal modelling. The spatio-temporal signal is decomposed as a linear combination of temporal basis elements with spatially dependent coefficients. The coefficients are then spatially modelled by ML algorithms (Deep Learning, ELM) with the help of a topographically-derived input feature space. Taking an advantage of an original UQ development for ELM, this decomposition allows UQ of the spatio-temporal predict ion . This methodology is applied on the Swiss wind speed data set, resulting in hourly time series of wind field maps at 250 meters spatial resolution, which is highly relevant for renewable energy potential assessment. The wind speed results are converted into wind energy potential used to support decision-making for renewable energy policies.
Newly developed open-source Python and R packages available on GitHub and CRAN repositories support the methodological contributions of the thesis, which can efficiently be applied to a variety of temporal, spatial, or spatio-temporal data.