A Physics-Informed Neural Network approach for compartmental epidemiological models

Area of Science:

• Epidemiology
• Computational Biology
• Machine Learning

Background:

• Compartmental models are essential for analyzing outbreak transmission, forecasting, and assessing interventions.
• Dynamic changes in awareness, interventions, and variants complicate accurate parameter estimation in epidemiological models.
• Time-varying transmission rates pose significant challenges for traditional modeling approaches.

Purpose of the Study:

• To introduce Physics-Informed Neural Networks (PINNs) for tracking temporal changes in epidemiological model parameters and state variables.
• To develop and evaluate a reduced-split approach for PINN implementation in epidemiological modeling.
• To assess the performance of PINNs in estimating time-varying transmission rates and predicting epidemic dynamics.

Main Methods:

• Utilized Physics-Informed Neural Networks (PINNs) to incorporate both data and system governing equations.
• Developed a novel reduced-split training strategy for PINNs, separating data and equation residual training.
• Applied the method to SIR model equations using synthetic data and real-world COVID-19 pandemic data from Italy.

Main Results:

• The split PINN approach demonstrated superior accuracy, achieving up to one order of magnitude improvement over joint methods.
• Achieved a 20% computational speed-up compared to traditional joint training approaches.
• Validated the method's effectiveness on synthetic datasets and real-world epidemic scenarios.

Conclusions:

• The proposed split PINN method offers a robust and efficient solution for estimating time-varying epidemiological parameters.
• PINNs provide a powerful tool for addressing ill-posed inverse problems in epidemic modeling.
• The method shows promise for accurate short-term forecasting of epidemic trajectories.