Comparative Modeling of Nuclear Energy Consumption in the United States and France: An Optimized Structure-Adaptive Grey Model

This study investigates nuclear energy consumption trends in the United States, and France by applying advanced time-series modeling and computational optimization techniques. Using annual consumption data from 2005 to 2023, the research compares the predictive accuracy under data scarcity of the AutoRegressive Integrated Moving Average (ARIMA), Grey Model (1,1,t), Grey Model(1,1,t²), and an Optimized Structure-Adaptive Grey Model (OSGM). This OSGM (1,1,t\(\:{}^{\lambda\:})\:\)extends the traditional Grey Model (1,1) by introducing time-dependent terms and parameter tuning through particle swarm optimization and Monte Carlo simulations. Models are trained and tested using an in-sample and out-of-sample period framework. Then, forecast accuracies are compared using Mean Absolute Percentage Error, and the Root Mean Squared Error. The results show that the new Optimized Structured Grey Model and the ARIMA models surpass the other models in achieving accuracy forecasts. While ARIMA performs well with sufficient data, the OSGM model, however, offers greater adaptability to nonlinear patterns and structural shifts, adapting to country-specific dynamics. The integration of informatics-driven optimization into grey system modeling presents a viable approach for energy forecasting in data-constrained environments. These results validate the model's suitability for situations with limited data and offer a useful tool for climate-aligned decision-making and sustainable energy planning.