用物理约束神经网络分析德国各州三年新冠传播，精准追踪各地疫情变化。
Modeling COVID-19 Dynamics in German States Using Physics-Informed Neural Networks
- 用物理信息神经网络反推感染数据，融合真实观测与流行病学模型。
- 揭示德国各州传播率差异显著，与疫苗接种率和疫情阶段密切相关。
- 适合做区域疫情建模、公共卫生决策的科研人员参考。
新冠疫情凸显了定量建模在理解真实世界疾病动态中的重要性。传统基于分室模型（如SIR）的回顾性分析虽能评估公共卫生干预措施的效果，但难以直接融入噪声较大的观测数据。本文采用物理信息神经网络（PINNs）求解SIR模型的逆问题，利用德国罗伯特·科赫研究所（RKI）的感染数据，对德国所有联邦州近三年的新冠传播动态进行了精细化时空分析。通过估计各州特有的传播率与恢复率参数，以及随时间变化的基本再生数（R_t），实现了对疫情演变过程的持续追踪。结果表明，各地区传播行为存在显著差异，且与疫苗接种水平及重大疫情阶段呈现相关性。研究证明了PINNs在局部、长期流行病学建模中的有效性。
原文摘要 · Abstract (English)
The COVID-19 pandemic has highlighted the need for quantitative modeling and analysis to understand real-world disease dynamics. In particular, post hoc analyses using compartmental models offer valuable insights into the effectiveness of public health interventions, such as vaccination strategies and containment policies. However, such compartmental models like SIR (Susceptible-Infectious-Recovered) often face limitations in directly incorporating noisy observational data. In this work, we employ Physics-Informed Neural Networks (PINNs) to solve the inverse problem of the SIR model using infection data from the Robert Koch Institute (RKI). Our main contribution is a fine-grained, spatio-temporal analysis of COVID-19 dynamics across all German federal states over a three-year period. We estimate state-specific transmission and recovery parameters and time-varying reproduction number (R_t) to track the pandemic progression. The results highlight strong variations in transmission behavior across regions, revealing correlations with vaccination uptake and temporal patterns associated with major pandemic phases. Our findings demonstrate the utility of PINNs in localized, long-term epidemiological modeling.
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