Predicting CO 2 Emissions with Advanced Deep Learning Models and a Hybrid Greylag Goose Optimization Algorithm

Global carbon dioxide (CO 2 ) emissions are increasing and present substantial environmental sustainability challenges, requiring the development of accurate predictive models. Due to the non-linear and temporal nature of emissions data, traditional machine learning methods—which work well when data are structured—struggle to provide effective predictions. In this paper, we propose a general framework that combines advanced deep learning models (such as GRU, Bidirectional GRU (BIGRU), Stacked GRU, and Attention-based BIGRU) with a novel hybridized optimization algorithm, GGBERO, which is a combination of Greylag Goose Optimization (GGO) and Al-Biruni Earth Radius (BER). First, experiments showed that ensemble machine learning models such as CatBoost and Gradient Boosting addressed static features effectively, while time-dependent patterns proved more challenging to predict. Transitioning to recurrent neural network architectures, mainly BIGRU, enabled the modeling of sequential dependence on emissions data. The empirical results show that the GGBERO-optimized BIGRU model produced a Mean Squared Error (MSE) of 1.0 × 10 −5 , the best tested approach. Statistical methods like the Wilcoxon Signed Rank Test and ANOVA were employed to validate the framework’s effectiveness in improving the evaluation, confirming the significance and robustness of the improvements due to the framework. In addition to improving the accuracy of CO 2 emissions forecasting, this integrated approach delivers interpretable explanations of the significant factors of CO 2 emissions, aiding policymakers and researchers focused on climate change mitigation in data-driven decision-making.