Modeling Natural Disaster via Unbalanced Regularized Optimal Transport

Natural disasters have far-reaching consequences that evolve across time and geography, requiring robust methods for analyzing their spatio-temporal impacts. This short paper introduces a novel framework based on unbalanced regularized optimal transport to model the redistribution of quarterly mortality rates from 2000-Q1 to 2024-Q4, applying our proposal to the International Emergency Events Database (EM-DAT). By discretizing disaster-affected regions into a geographic grid, we track how mortality distributions shift between consecutive quarters, accounting for imbalanced datasets where the total mass (e.g., deaths) varies over time. The unbalanced optimal transport formulation enables the modeling of changes in both population distribution and disaster severity, while entropy regularization ensures computational efficiency and robustness to noise. Our results reveal significant spatio-temporal patterns in mortality distributions, identifying regions of heightened vulnerability and potential drivers behind these changes.