Aquaformer: Multi-source transfer learning model based on Transformer and phase space reconstruction for long sequence water quality forecasting

Smart water management relies on in-situ water quality data with long-term forecasts to support decision-making. Despite this urgent demand, the state-of-the-art methods for long sequence time-series forecasting haven’t been widely applied to smart water management and tuned for water quality forecasting. This study proposes Aquaformer, a Transformer-based model oriented to smart water management, where phase space reconstruction (PSR) is coupled with transfer learning to cope with the perennial data scarcity issue. Water quality data could be considered observations of the trajectories of high-dimensional water quality phase space, sharing the same dynamics with the systems reconstructed from the observations. Redefining the problem based on PSR could improve interpretability and reduce sequence length. The multi-source domain should follow dynamics similar to those of the corresponding target domain and thus consist of more correlated data. The experiments on 5 datasets of varied sizes showed that compared with baseline models, Aquaformer had the highest efficiency and achieved best performance in 41 out of 45 scenarios, reducing prediction error by 10.08 ∼ 39.52 %. Meanwhile, its transfer strategy had superior transfer gain to the alternatives with an average over 14 %. The sparse attention module and prediction calibrator of Aquaformer also proved effective in ablation studies.