Developing Surrogates for Epidemic Agent-Based Models via Scientific Machine Learning

Forecasting epidemic trajectories is challenging due to nonlinear dynamics, abrupt interventions, and limited data. Classical compartmental models are interpretable but rigid, while purely data-driven methods often lack physical consistency. We propose a hybrid framework based on Universal Differential Equations (UDEs), which augment epidemiological Ordinary Differential Equations (ODEs) with neural networks to capture unresolved dynamics. To overcome instability in standard single-shooting training, we introduce two advances: (i) a multiple-shooting (MS) scheme that segments trajectories and enforces continuity across intervals, and (ii) a prediction error method that iteratively corrects forward simulations. Applied to epidemic datasets, our approach reduces symptomatic prediction error by 77.8\% with multiple shooting and 82.1\% with the prediction error method (PEM), particularly around intervention periods such as lockdowns. Multiple shooting improves stability and efficiency, while the prediction error method achieves the most accurate ground-truth alignment at a higher computational cost. These results demonstrate how MS and PEM methods could improve the fitting of UDEs, which will help bridge the gap between purely mechanistic models and agent-based models, and enable interpretable and accurate epidemic forecasting.