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.

翻译：我们提出了一种Koopman增强的物理信息神经网络（K--PINN）框架，用于非线性传染病模型中的参数推断与预测。该方法将Koopman算子理论与物理信息学习相结合，通过将传染病状态映射至潜在可观测量空间，使动力学演化近似线性化，同时利用自动微分满足控制传染病方程。这种集成方式提升了模型的可解释性、参数可辨识性及长期预测稳定性。我们将该框架应用于标准化的SEIRSD传染病模型，并利用合成猴痘（Mpox）数据以及来自德国、摩洛哥和瑞典的SARS-CoV-2真实数据集进行验证。合成轨迹通过保持结构的非标准有限差分格式生成，以确保可靠的训练数据。数值结果表明，与经典PINN和Koopman-EDMD方法相比，K--PINN能够实现更精确的参数估计、轨迹重构和长期预测。这些结果表明，K--PINN是一种有效的传染病建模机器学习框架，可扩展至更复杂的系统。