With the manufacturing reshoring to the US, increasing attention are focus on its energy consumption and environmental effects and accurate prediction of carbon emissions is vital to controlling growth from the source. Considering the slowing growth in carbon emissions with the Gompertz's law, this paper establishes a Gompertz differential equation. According to the differential information principle and fractional accumulation operator, this differential equation is transformed into a fractional accumulation grey Gompertz model. Furthermore, the chaotic whale optimization algorithm is used to optimize the order of accumulation generation and the grey background value in the proposed model. Then the Gompertz's datasets and six validation cases about carbon emissions are used to show that the proposed model demonstrates better accuracy in all cases and efficiency in the carbon emissions forecasting with several existing models. Three case studies indicate that the proposed model can fit the trend of American industrial carbon emissions better. The model results also reveal the recent policy changes have promoted the uptrend of the industrial and the total carbon emissions in the U.S. The future forecasting suggests that U.S. carbon emission is estimated to be 17.01% (in total emissions) or 17.89% (in industrial emission) percent below 2005 levels by 2025 under current policies, falling short of its commitment submitted to the United Nations Framework Convention on Climate Change.

随着制造业向美国转移，其能源消耗和环境影响越来越受到关注，准确预测碳排放对于从源头控制增长至关重要。根据Gompertz定律，考虑到碳排放增长放缓，本文建立了Gompertz微分方程。根据微分信息原理和分数累加算子，将该微分方程转化为分数累加灰色Gompertz模型。此外，在所提出的模型中，使用混沌鲸鱼优化算法来优化累积生成顺序和灰色背景值。然后是 Gompertz' s 数据集和六个关于碳排放的验证案例被用来表明所提出的模型在所有情况下都表现出更好的准确性，并且在几个现有模型的碳排放预测中表现出更高的效率。三个案例研究表明，所提出的模型能够更好地适应美国工业​​碳排放的趋势。模型结果还揭示了近期的政策变化促进了美国工业和总碳排放量的上升趋势 未来预测表明美国碳排放量估计为 17.01%（占总排放量）或 17.89%（占工业排放量） ) 在当前政策下，到 2025 年低于 2005 年水平的百分比，未达到其提交给联合国气候变化框架公约的承诺。