标题： 代数可观测的物理信息神经网络及其在流行病学建模中的应用 显示英文标题

标题： Algebraically Observable Physics-Informed Neural Network and its Application to Epidemiological Modelling

摘要： 物理信息神经网络（PINN）是一种将数据背后的控制方程整合到损失函数中的深度学习框架。 在本研究中，我们考虑使用PINN来估计由常微分方程描述的流行病学模型中的状态变量和参数问题。 实际上，并非所有由模型描述的人口轨迹数据都可以被测量。 利用部分测量数据学习PINN来估计未测量的状态变量和流行病学参数是具有挑战性的。 因此，我们引入了状态变量的代数可观测性概念。 具体来说，我们提出了基于代数可观测性分析来增强未测量数据的方法。 所提出的方法在流行病学建模的三种情境下的数值实验中得到了验证。 具体而言，给定带有噪声和部分测量数据，所提出方法在未测量状态和参数估计的准确性方面优于传统方法。 所提出的方法在实际场景中也被证明是有效的，例如当某些变量的数据无法从测量中重建时。 显示英文摘要

摘要： Physics-Informed Neural Network (PINN) is a deep learning framework that integrates the governing equations underlying data into a loss function. In this study, we consider the problem of estimating state variables and parameters in epidemiological models governed by ordinary differential equations using PINNs. In practice, not all trajectory data corresponding to the population described by models can be measured. Learning PINNs to estimate the unmeasured state variables and epidemiological parameters using partial measurements is challenging. Accordingly, we introduce the concept of algebraic observability of the state variables. Specifically, we propose augmenting the unmeasured data based on algebraic observability analysis. The validity of the proposed method is demonstrated through numerical experiments under three scenarios in the context of epidemiological modelling. Specifically, given noisy and partial measurements, the accuracy of unmeasured states and parameter estimation of the proposed method is shown to be higher than that of the conventional methods. The proposed method is also shown to be effective in practical scenarios, such as when the data corresponding to certain variables cannot be reconstructed from the measurements.