With the growing severity of global climate change, forecasting and managing carbon dioxide (CO₂) emissions has become one of the critical tasks in addressing climate change. To improve the accuracy of CO₂ emission forecasting, an innovative framework based on variational mode decomposition (VMD), improved black-winged kite algorithm (IBKA), and BiLSTM networks is proposed. This framework aims to address the challenges associated with predicting non-stationary data and optimizing model hyperparameters. Initially, experiments were conducted on 29 benchmark functions using the IBKA algorithm, demonstrating its superior performance in highly nonlinear and complex environments. Subsequently, the BiLSTM model optimized by IBKA was employed to predict CO₂ emission trends across four major industries in China, confirming its enhanced prediction accuracy. Finally, a comparative analysis with other mainstream machine learning and deep learning models revealed that the BiLSTM model consistently achieved the best predictive performance across all industries. This research proposes an efficient and practical technical pathway for intelligent carbon emission prediction under the “dual-carbon” strategic goals, offering scientific support for policy formulation and the low-carbon transition.

The highly stochastic nature of rainfall presents significant challenges for the accurate prediction of its time series. To enhance the prediction performance of non-stationary rainfall time series, this study proposes a hybrid deep learning forecasting framework—VMD-IWMA-BiLSTM—that integrates Variational Mode Decomposition (VMD), Improved Whale Migration Algorithm (IWMA), and Bidirectional Long Short-Term Memory network (BiLSTM). Firstly, VMD is employed to decompose the original rainfall series into multiple modes, extracting Intrinsic Mode Functions (IMFs) with more stable frequency characteristics. Secondly, IWMA is utilized to globally optimize multiple hyperparameters of the BiLSTM model, enhancing its ability to capture complex nonlinear relationships and long-term dependencies. Finally, experimental validation is conducted using daily rainfall data from 2020 to 2024 at the Xinzheng National Meteorological Observatory. The results demonstrate that the proposed framework outperforms traditional models such as LSTM, ARIMA, SVM, and LSSVM in terms of prediction accuracy. This research provides new insights and effective technical pathways for improving rainfall time series prediction accuracy and addressing the challenges posed by high randomness.