基于物理信息神经网络的传染病模型时变参数反演

Inversion of Time-Varying Parameters in Epidemic Models via Physics-Informed Neural Network

摘要: 机理模型在面对不完整的数据时，难以准确识别动态变化的未知参数。同时，纯数据驱动的深度学习模型也缺乏底层物理规律的有效约束。为了克服这些缺陷，构建了一种基于物理信息神经网络的参数反演框架，该计算框架将传染病动力学方程转化为数学残差项，并将其直接嵌入到深度网络的全局损失函数之中。通过选取马来西亚连续一百二十天的公共卫生事件相关真实数据进行分析，实验利用两个相互独立的前馈神经网络分别逼近真实的流行病数据与时变参数。研究结果表明，该算法能够有效过滤现实统计数据中的高频噪声，实现对状态变量的高度拟合，并推导出变化的传染率演化过程。这种结合物理机理和统计数据的方法，有效解决数据缺失条件下的参数计算难题，为复杂的流行病学动态预测提供可靠的分析工具。

Abstract: Mechanism-based models face difficulties in accurately identifying dynamically changing unknown parameters when dealing with incomplete data. Simultaneously, purely data-driven deep learning models lack the effective constraints of underlying physical laws. To overcome these defects, a parameter inversion framework based on physics-informed neural networks is constructed. This computational framework transforms epidemic dynamic equations into mathematical residual terms and directly embeds them into the global loss function of the deep network. By analyzing real epidemic data from Malaysia for 120 consecutive days, the experiment utilizes two independent feedforward neural networks to approximate the actual epidemiological data and the time-varying parameters respectively. The research results indicate that this algorithm can effectively filter high-frequency noise in real statistical data, achieve high-precision fitting for state variables, and derive the evolutionary process of the varying transmission rate. This method combining physical mechanisms and statistical data effectively solves the parameter calculation problem under data-deficiency conditions. This framework provides a reliable analytical tool for complex epidemiological dynamic forecasting.