Deep learning methods and evaluation of the extensive carbon emission predictive solution for Danish grid

Abstract

The increase in industrialization and the rise of large commercial cities have significantly contributed to the escalation of carbon emissions over the last few centuries. Accurate forecasting of carbon emissions is critical for governing bodies to implement effective policies aimed at promoting sustainable development. This study investigates both deterministic and probabilistic forecasting models, assessing their prediction accuracy and reliability. The deterministic models applied four deep learning algorithms—Convolutional Neural Networks (CNN), Deep Feedforward Neural Networks (DFNN), Long Short-Term Memory (LSTM), and Multi-Headed Attention LSTM (MHA-LSTM). Probabilistic forecasting models were further enhanced using Monte Carlo simulations (MCS). The performance of these algorithms was evaluated across multiple metrics. MHA-LSTM demonstrated superior performance in both deterministic and probabilistic forecasting. In deterministic predictions, it achieved the lowest Mean Absolute Error (MAE) at 0.014 during training and 0.017 during testing, outperforming CNN, DFNN, and LSTM. It also recorded minimal Mean Squared Error (MSE) and Mean Absolute Percentage Error (MAPE). In probabilistic forecasting, Attention LSTM excelled with the lowest Absolute Calibration Error (ACE%) at -0.150 and Interval Score (IS) of $-2.892\times 10^5$, significantly outperforming other models. Its strong performance across metrics and confidence levels, particularly in Pinball metrics for prediction bounds, highlights its robustness and accuracy, making it ideal for carbon emission forecasting and policy planning.