Multi-source variational mode transfer learning for enhanced PM2.5 concentration forecasting at data-limited monitoring stations

Hybrid methods combining data decomposition with deep learning have recently exhibited remarkable performance in PM2.5 concentration forecasting. However, these methods still encounter limitations when confronted with monitoring sites lacking adequate historical data. To overcome this challenge, this study proposes a novel methodological framework named as Multi-source Variational Mode Transfer Learning (MSVMTL) that integrates data decomposition, deep learning, and multi-source transfer learning strategies. The framework consists of four stages: source domain selection, data decomposition by Variational Mode Decomposition (VMD), mode sequence clustering, and multi-source mode transfer learning. The source domain selection stage utilizes EMS (Euclidean Distance and Maximum Mean Discrepancy Distance) to identify the most suitable source domain for knowledge transfer. The mode sequence clustering employs the LDDK algorithm (Largest Triangle Three Buckets, Dynamic Time Warping, Dynamic Time Warping Barycenter Averaging, and K-means) to cluster modes from VMD-derived domains. The multi-source mode transfer stage combines VMD with pre-training and fine-tuning, leveraging source domain knowledge for target domain prediction. To validate the proposed framework, a case study, including multiple sets of comparative experiments and ablation study, was conducted using data from 12 air quality monitoring sites in Beijing, China. The experimental results demonstrate that EMS, LDDK, and multi-source mode transfer learning strategy all achieved excellent performance, and the presented MSVMTL significantly enhances the prediction accuracy of PM2.5 concentrations at monitoring sites with limited historical data.