DGPAEP-Net: Deep Gaussian process network with approximate expectation propagation for carbon emission prediction in municipal wastewater treatment processes
Yonglin Li, Yongmu Li, Kun Zheng, Chao Meng, Changjian Zhu, Zenghai Shan · Digital engineering. · 2025
Excessive carbon emissions exacerbate climate change and biodiversity loss, making carbon emission monitoring a global environmental focus. Advances in machine learning offer new perspectives for addressing excessive carbon emissions. This study employs an improved Bayesian neural network-based machine learning model to predict carbon emissions, using a full-scale wastewater treatment plant in eastern China as an example. The enhanced model introduces a novel and robust deterministic approximation scheme, leveraging an approximate expectation propagation algorithm and a fully independent training condition approximation to overcome computational and analytical challenges. This model is termed the deep Gaussian process network with approximate expectation propagation (DGPAEP). Before the formal carbon emission prediction, the model's generalization capability was benchmarked against other state-of-the-art Bayesian neural networks on public datasets, ensuring its high performance. Experimental results demonstrate that, compared to other Bayesian neural networks, DGPAEP achieved an increase of 149.07 % in the average test log-likelihood and a 3.05 % reduction in root mean square error. To explore the contribution of different features to the predictive values, Shapley additive explanations (SHAP) were utilized to quantify their impact on the output, thereby better-guiding emission reduction efforts. These findings suggest that machine learning models have the potential to establish a robust framework to enhance the prediction capabilities of carbon emissions in wastewater treatment, offering a promising approach for real-time monitoring and scientific reduction of carbon emissions in wastewater treatment plants.