PDE-Informed Gradient Boosting for Disease Outbreak Detection and Forecasting

Accurate forecasting of disease outbreaks in space and time remains a major challenge in epidemiology, particularly when data is sparse, noisy, or lacks fine-grained resolution. This paper introduces a novel framework that integrates the physical principles of epidemic dynamics, expressed through partial differential equations (PDEs), into the feature engineering process of a Gradient Boosting Machine (GBM). By extracting physically meaningful quantities, such as spatial gradients, Laplacians, temporal derivatives, and PDE residuals, from simulated PDE models, the proposed method augments the feature space with domain-informed variables that enhance predictive performance. We develop a complete mathematical foundation for this approach and demonstrate how it can be used for both disease forecasting and risk classification tasks. This PDE-informed boosting framework bridges the gap between mechanistic modeling and modern machine learning, offering interpretable, efficient, and accurate epidemic modeling.