基于最优传输理论的碳中和问题的模型构建研究

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。

ENTROPICAL OPTIMAL TRANSPORT,SCHRODINGER'S SYSTEM AND ALGORITHMS

In this exposition paper we present the optimal transport problem of Monge-Ampère-Kantorovitch(MAK in short)and its approximative entropical regularization.Contrary to the MAK optimal transport problem,the solution of the entropical optimal transport problem is always unique,and is characterized by the Schrödinger system.The relationship between the Schrödinger system,the associated Bernstein process and the optimal transport was developed by Léonard[32,33](and by Mikami[39]earlier via an h-process).We present Sinkhorn’s algorithm for solving the Schrödinger system and the recent results on its convergence rate.We study the gradient descent algorithm based on the dual optimal question and prove its exponential convergence,whose rate might be independent of the regularization constant.This exposition is motivated by recent applications of optimal transport to different domains such as machine learning,image processing,econometrics,astrophysics etc..