Differential equation model of carbon dioxide emission using functional linear regression

Carbon dioxide is one of the major contributors to Global Warming. In the present study, we develop a differential equation to model the carbon dioxide emission data in the atmosphere using functional linear regression approach. In the proposed method, a differential operator is defined as data smoother and we use the penalized least square fitting criteria to smooth the data. The profile error sum of squares is optimized to estimate the differential operators using functional regression. The solution of the developed differential equation estimates and predicts the rate of change of carbon dioxide in the atmosphere at a particular time. We apply the proposed model to fit the emission of carbon dioxide data in the continental United States. Numerical simulations of a number of test cases depict a satisfactory agreement with real data.二氧化碳是引发全球变暖的主要贡献因子之一。本研究采用函数型线性回归（functional linear regression）方法，构建微分方程以对大气中的二氧化碳排放数据开展建模工作。在所提出的方法中，我们将微分算子定义为数据平滑器，并采用惩罚最小二乘（penalized least square）拟合准则完成数据平滑处理。借助函数型回归，通过优化轮廓误差平方和来实现微分算子的估计。所构建微分方程的解可用于估计并预测特定时刻大气中二氧化碳的变化速率。我们将所提模型应用于美国本土的二氧化碳排放数据拟合任务。多组测试案例的数值仿真结果显示，模型输出与真实数据之间具有令人满意的吻合度。