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[Display omitted] • A novel structure-adaptative grey model with a time power is proposed. • The Cultural Algorithm is employed for determining the optimal time power item. • Monte-Carlo Simulation and Probability Density Analysis are originally introduced to enhance the model's robustness. • Empirical results comprehensively verify the efficacy of our novel method. • The future demands for nuclear energy are predicted by using the promising model from 2019 to 2023. Accurate estimations of nuclear energy consumption are an essential process for formulating appropriate policies and plans in the energy sector and associated companies. This paper presents a novel structure-adaptive grey model with an adjustable time power based on the nonlinear and complicated characteristics of nuclear energy consumption, in which three core innovations are summarized below. Initially, the generalized time response function for projections is theoretically deduced, which overcomes the fundamental flaws in the conventional grey model. Subsequently, the Cultural Algorithm is employed to determine the optimum values of the time power item to improve the adaptability and flexibility to confront diverse forecasting issues. Further, Monte-Carlo Simulation and Probability Density Analysis (PDA) are originally introduced to enhance the robustness of the proposed model. For illustration and verification purposes, experiments on predicting nuclear energy consumption in China and America are conducted in comparison with a range of benchmark models, including other prevalent grey models, conventional econometric technology, and artificial intelligences. The performance of the novel technique is evaluated from two different perspectives of PDA and level accuracy, confirming that this model is a very promising and powerful tool for predicting nuclear energy demands in China and America from 2019 to 2023. [ABSTRACT FROM AUTHOR]