Neural Networks for Robust Extreme Event Forecasting: Theory and Applications

Abstract

This thesis explores the efficacy of data-driven generative learning approaches, with a particular focus on extreme value theory (EVT) and its applications in predictive modeling. We begin by addressing the limitations of existing extreme value distribution models, proposing novel methods for accurately representing extreme events in statistical processes. Our first contribution is a robust, generative approach to modeling multivariate extreme value (MEV) distributions, improving the accuracy and reliability of risk estimates. We then extend this work by introducing a representation learning framework that leverages max-stability principles to enhance the extrapolation of rare events in high-dimensional settings. To demonstrate the practical impact of our methods, we apply generative learning to predictive maintenance, focusing on vehicle failure forecasting using real-world sensor data from the U.S. Army’s Condition-Based Maintenance+ (CBM) program. By integrating EVT principles with generative models, we provide a novel, data-driven solution for anticipating mechanical failures and optimizing fleet maintenance policies. Our findings highlight the potential of generative learning to enhance the robustness of extreme event prediction, ensuring more reliable risk assessments and decision-making in various domains, including finance, engineering, and health sciences.