Abstract: Global warming has become the focus of today’s society. The main cause of global warming is the massive emission of greenhouse gases such as carbon dioxide. China proposed the target for carbon peak and carbon neutrality, which provides a specific idea for further solving the global warming. Carbon peak refers to the fact that the carbon emission reaches the maximum at a certain time. Carbon neutrality refers to the total amount of carbon dioxide or greenhouse gas emission produced by the country, enterprise, product, activity or individual directly or indirectly within a certain period of time, which can be offset by afforestation, energy conservation and emission reduction to achieve positive and negative offset, and relative “zero emission”. Generally, the targets of carbon peak and carbon neutrality are referred to as the “double carbon” target.
How to realize the energy transfer between the source and sink of carbon emission and carbon absorption effectively is the core issue of the research on carbon neutrality theory. The optimal transport theory is to find the optimal distribution calculation of the joint probability distribution field of the source and sink at the minimum cost. This research mode provides a new research perspective for dealing with the carbon neutrality problem.
In this paper, the Kantorovich form problem in the optimal transport theory is taken as the basic model, and the content of probability distribution information in mathematical statistics is combined to explore the process of model establishment and method solving about carbon neutrality related problems. Since the acquisition of comprehensive data on carbon emission and carbon absorption is costly and involves internal information of enterprise, it is generally not published directly. Therefore, according to the data information obtained in the statistical yearbook, relevant literature and materials, and in combination with the actual development situation, the hypothesis of using Weibull distribution and Normal distribution to describe the distribution form of carbon emission and carbon absorption respectively is put forward in the process of numerical simulation.
In the first part, based on the relationship between carbon emission and its influencing factors, the exponential distribution family is used to describe the distribution form satisfied by carbon emission. Combining the prior distribution of parameter constructed by the generalized linear model and the posterior idea of Bayesian distribution, the accurate estimation of parameter is obtained according to the Lagrange function and the maximum likelihood estimation method. And then the marginal probability distribution satisfied by carbon emission is obtained. At the same time, the distribution of relevant measurable data in the process of carbon absorption is obtained based on the experiment of industry data, so as to know the specific distribution information of carbon source and carbon sink.
In the second part, according to the actual change, it is not difficult to find that the balanced development and path selection between carbon emission and carbon absorption can provide a reasonable plan and effective strategy for achieving the target of carbon neutrality, which is consistent with the idea of energy conservation in the optimal transport theory. Therefore, the distribution information of carbon emission and carbon absorption is considered as the marginal distribution, and the form of Kantorovich problem in the optimal transport theory is integrated to construct the optimal transport model with the constraint of carbon neutrality, which can express and deal with carbon related problems in a clearer way.
In the third part, in order to modify the model, the regression analysis method is used to test the relationship between target system and prediction system, and the system parameter is fed back and adjusted according to the result obtained by minimizing the loss function, so as to obtain a better transmission system.
In the last part, the feasibility and effectiveness of the proposed model and method are verified by numerical simulation. In this process, the coupling distribution between carbon source and carbon sink and the target optimal value can be obtained by using the Sinkhorn fast algorithm. At the same time, the specific transport plan between them can be visually displayed by the transport diagram.
In summary, the optimal transport theoretical model with carbon neutrality as a constraint can describe the correlation between carbon emission and carbon absorption reasonably and effectively. At the same time, the specific transport plan between the two can be solved by using a fast algorithm, which ensures the fitness of the solution for the established model. It is worth noting that the proposed idea provides an effective path selection and concrete implementation strategy for the final realization of carbon neutrality target, which has the theoretical significance and application value for quantitative analysis about related problems. In the following research, the carbon related issue will be considered in combination with the dynamic evolution, so that the distribution information is closer to the actual complex situation of the development and change of carbon emission and carbon absorption.

Key words: optimal transport, carbon neutrality, Bayesian distribution, Lagrange function, structural risk optimization, Sinkhorn algorithm

摘要： 全球变暖已经成为当今社会所关注的焦点问题,导致全球变暖的主要原因是二氧化碳等温室气体的大量排放,我国碳达峰与碳中和目标的提出为进一步解决全球气候变暖现象提供了具体思路。如何实现碳排放量与碳吸收量之间源与汇的有效能量传输是碳中和相关理论研究的核心问题。最优传输理论是以最小成本找到源与汇的联合概率分布场的最优分布计算,此种研究模式为处理碳中和问题提供了一个全新的研究视角。首先基于贝叶斯分布的后验思想与指数分布族的先验形式,利用Lagrange函数得到碳排放量所满足的边缘概率分布,并根据数据实验得出碳吸收量的分布形式,然后基于最优传输理论建立相应的碳中和模型,并利用回归分析方法对所得到的传输系统进行检验与调节,最后基于数值模拟证明所提出方法的可行性。此种将碳中和作为约束的最优传输模型,能够得到合理有效的碳排放与碳吸收之间的传输计划,具有定量化分析相关问题的理论意义与应用价值。

关键词: 最优传输, 碳中和, 贝叶斯分布, Lagrange函数, 结构风险优化, Sinkhorn算法