Computational and Statistical Advances in Spatio-Temporal Modeling: Causality, Deep Learning, and High-Performance Computing

Overview

First, we investigate spatial causality in spatio-temporal systems, proposing new methodologies to handle hidden confounding variables, extreme events, and structural nonlinearities. Second, we examine spatio-temporal forecasting for wind energy, exploring the application of advanced deep learning architectures, including deep echo state networks and graph autoencoders, to capture complex nonlinear wind patterns. Third, we address computational limitations of a special mathematical function, BesselK, which is widely used in Gaussian processes with Matérn kernel, by developing GPU-accelerated matrix generation algorithms for efficient processing of large-scale spatial datasets, particularly focusing on maximum likelihood estimation. Through comprehensive empirical validation using simulated and real-world datasets, we demonstrate the effectiveness of our proposed approaches. Our work contributes to environmental data science by addressing fundamental computational and methodological challenges in analyzing large-scale spatial and spatio-temporal datasets.