Improving pandemic prediction: integrating Physics-Informed Neural Networks and symbolic regression for COVID-19 modeling

This study refines the SIDARTHE model for Italy's COVID-19 outbreak using a hybrid, data-driven framework. A two-stage approach compares Maximum Likelihood Estimation (MLE) with Physics-Informed Neural Networks (PINNs) for parameter estimation, then applies Symbolic Regression (via gplearn and PySR) to optimize the governing equations. Results show PINNs surpass MLE in accuracy, and PySR outperforms gplearn in deriving robust expressions. The final integrated model-combining PINN estimation with Symbolic Regression-significantly reduces predictive uncertainty and aligns closely with observed data, providing a resilient tool for public health planning.