基于物理信息的函数连接极值理论在数据驱动的流行病房室模型参数发现中的应用
Physics-Informed Extreme Theory of Functional Connections Applied to Data-Driven Parameters Discovery of Epidemiological Compartmental Models
摘要：
在这项工作中，我们应用了一种新的，准确的，快速的，强大的物理信息神经网络框架，用于通过参数常微分方程（ODE）建模的问题的数据驱动参数发现，称为函数连接的极值理论（X-TFC）。所提出的方法合并了两个最近开发的框架，用于解决涉及参数DE的问题，1）功能连接理论（TFC）和2）物理信息神经网络（PINN）。特别是，这项工作的重点是能力的X-TFC在解决逆问题，通过确定性的方法来估计参数的流行病学房室模型。在这项工作中处理的流行病学房室模型是易感-感染-传染病（SIR），易感-暴露-传染病-传染病（SEIR）和易感-暴露-传染病-传染病-易感（SEIR）。结果表明，低的计算时间，高精度和有效性的X-TFC方法在执行数据驱动的参数发现的系统建模通过参数ODE使用未扰动和扰动数据。
英文摘要：
In this work we apply a novel, accurate, fast, and robust physics-informed neural network framework for data-driven parameters discovery of problems modeled via parametric ordinary differential equations (ODEs) called the Extreme Theory of Functional Connections (X-TFC). The proposed method merges two recently developed frameworks for solving problems involving parametric DEs, 1) the Theory of Functional Connections (TFC) and 2) the Physics-Informed Neural Networks (PINN). In particular, this work focuses on the capability of X-TFC in solving inverse problems to estimate the parameters governing the epidemiological compartmental models via a deterministic approach. The epidemiological compartmental models treated in this work are Susceptible-Infectious-Recovered (SIR), Susceptible-Exposed-Infectious-Recovered (SEIR), and Susceptible-Exposed-Infectious-Recovered-Susceptible (SEIR). The results show the low computational times, the high accuracy and effectiveness of the X-TFC method in performing data-driven parameters discovery of systems modeled via parametric ODEs using unperturbed and perturbed data.
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