论文标题
神经网络混合模型在估计非线性流行模型的感染功能中的应用
Application of neural-network hybrid models in estimating the infection functions of nonlinear epidemic models
论文作者
论文摘要
混合神经网络模型将神经网络拟合功能与微分方程模型的优势结合在一起，以反映实际的物理过程，并广泛用于分析时间序列数据。大多数相关研究都集中在线性混合模型上，但只有少数研究了非线性问题。在这项工作中，我们使用混合非线性流行性神经网络作为研究其在预测流行病模型正确感染功能方面的力量的入口点。为了实现这一目标，我们将非线性差异模型的分叉理论与于点误差损失和设计新型损耗函数相结合，以确保模型的训练性。此外，我们发现支持普通微分方程的独特存在条件以估计正确的感染功能。使用Runge Kutta方法，我们在提出的模型上执行数值实验并验证其声音。我们还将其应用于实际的Covid-19数据，以准确发现其感染性的变化定律。
Hybrid neural network models combine the advantages of a neural network's fitting functionality with differential equation models to reflect actual physical processes and are widely used in analyzing time-series data. Most related studies have focused on linear hybrid models, but only a few have examined nonlinear problems. In this work, we use a hybrid nonlinear epidemic neural network as the entry point to study its power in predicting the correct infection function of an epidemic model. To achieve this goal, we combine the bifurcation theory of the nonlinear differential model with the mean-squared error loss and design a novel loss function to ensure model trainability. Furthermore, we find the unique existence conditions supporting ordinary differential equations to estimate the correct infection function. Using the Runge Kutta method, we perform numerical experiments on our proposed model and verify its soundness. We also apply it to real COVID-19 data to accurately discover the change law of its infectivity.
