Forecasting Seasonal Influenza Epidemics with Physics-Informed Neural Networks

TL;DR

This paper introduces SIR-INN, a physics-informed neural network model that integrates the SIR epidemic model to provide accurate, real-time influenza forecasts with uncertainty quantification, trained on synthetic data and validated on Italian influenza seasons.

Contribution

The paper presents a novel hybrid neural network framework that combines mechanistic epidemic modeling with machine learning, enabling generalizable and efficient influenza forecasting.

Findings

SIR-INN performs competitively with state-of-the-art methods in influenza forecasting.

The model provides accurate predictions across different outbreak phases.

Uncertainty intervals are reliably maintained, though calibration can be improved.

Abstract

Accurate epidemic forecasting is critical for informing public health decisions and timely interventions. While Physics-Informed Neural Networks have shown promise in various scientific domains, their potential application to real-time epidemic forecasting remains underexplored. Here, we present SIR-INN, a hybrid forecasting framework that integrates the mechanistic structure of the classical Susceptible-Infectious-Recovered (SIR) model into a neural network architecture. Trained once on synthetic epidemic scenarios, the model is able to generalize across epidemic conditions without retraining. From limited and noisy observations, SIR-INN infers key transmission parameters via Markov chain Monte Carlo, generating probabilistic short- and long-term forecasts. We validate SIR-INN using national influenza data from the Italian National Institute of Health in the 2023-2024 and 2024-2025 seasons. The model performs competitively with current state-of-the-art approaches, particularly in terms of Weighted Interval Score. It shows accurate predictive performance in nearly all phases of the outbreak, with improved accuracy observed for the 2024-2025 influenza season. Credible uncertainty intervals are consistently maintained, while coverage metrics highlight room for improvement in uncertainty calibration. SIR-INN offers a computationally efficient, transparent, and generalizable solution for epidemic forecasting, appropriately leveraging the framework's hybrid design. Its ability to provide real-time predictions of epidemic dynamics, together with uncertainty quantification, makes it a promising tool for real-world epidemic forecasting.