A Koopman-PINN Framework for Epidemic Models: Parameter Inference and Forecasting

2026-06-13

AI Summary

This study addresses the challenges of parameter identifiability, long-term prediction instability, and limited interpretability in nonlinear epidemic models by proposing a novel integration of Koopman operator theory with physics-informed neural networks (PINNs). The approach embeds epidemic dynamics as hard constraints via automatic differentiation and leverages structure-preserving nonstandard finite difference schemes to generate high-fidelity training data. By lifting the system into a latent observable space where evolution is approximately linear, the method substantially enhances both parameter identifiability and long-term predictive stability while improving model interpretability. Comprehensive experiments on synthetic mpox data and real-world COVID-19 datasets from Germany, Morocco, and Switzerland demonstrate that the proposed framework consistently outperforms conventional PINNs and Koopman-EDMD methods in parameter estimation, trajectory reconstruction, and long-range forecasting.

Abstract

We propose a Koopman-enhanced physics-informed neural network (K--PINN) framework for parameter inference and forecasting in nonlinear epidemic models. This method combines Koopman operator theory and physics-informed learning. It maps epidemic states into a latent observable space where the dynamics evolve approximately linearly while satisfying the governing epidemic equations through automatic differentiation. This integration improves interpretability, parameter identifiability, and long-term predictive stability. We apply the proposed framework to a normalized SEIRSD epidemic model and evaluate it using synthetic monkeypox (Mpox) data and real-world datasets from Germany, Morocco, and Sweden for the SARS-CoV-2 virus. Synthetic trajectories are generated using a structure-preserving, nonstandard finite difference scheme to ensure reliable training data. Numerical results demonstrate that K--PINN achieves more accurate parameter estimation, trajectory reconstruction, and long-term forecasting than classical PINNs and Koopman-EDMD approaches. These results suggest that K--PINN is an effective machine learning framework for epidemic modeling that can be extended to more complex systems.

Problem

• epidemic models
• parameter inference
• forecasting
• nonlinear dynamics
• Koopman operator

Innovation

• Koopman operator
• physics-informed neural networks
• epidemic modeling
• parameter inference
• nonlinear dynamics