A physics-informed neural network (PINN) embedded with the susceptible-infected-removed (SIR) model is devised to understand the temporal evolution dynamics of infectious diseases. Firstly, the effectiveness of this approach is demonstrated on synthetic data as generated from the numerical solution of the susceptible-asymptomatic-infected-recovered-dead (SAIRD) model. Then, the method is applied to COVID-19 data reported for Germany and shows that it can accurately identify and predict virus spread trends. The results indicate that an incomplete physics-informed model can approach more complicated dynamics efficiently. Thus, the present work demonstrates the high potential of using machine learning methods, e.g., PINNs, to study and predict epidemic dynamics in combination with compartmental models.

翻译：本文构建了一种嵌入易感-感染-移除（SIR）模型的物理信息神经网络（PINN），用于理解传染病的时序演化动力学。首先，通过易感-无症状-感染-康复-死亡（SAIRD）模型数值解生成的合成数据验证了该方法的有效性。随后将该方法应用于德国报告的COVID-19数据，结果表明其能准确识别并预测病毒传播趋势。研究发现，不完整的物理信息模型能够高效逼近更复杂的动力学过程。本研究充分展示了将机器学习方法（如PINN）与区间模型相结合，用于研究和预测流行病动力学的巨大潜力。