Inverse-distance weighting alignment-diversity attention transformer for days ahead particulate matter concentration forecasting

An accurate forecasting of the particulate matter (PM) concentrations including PM2.5 and PM10 concentrations is vital for the publichealth and the environment management. Forecasting highly non-stationary PM time series is challenging due to their complex spatialand temporal dependencies and irregular local correlations. In this paper, an adaptive Inverse-Distance Weighting (IDW) iTransformer-based framework referred to as IDW-ADAFormer is devised for the medium-term joint forecasting of spatially distributed multi-sensorPM data. In particular, the adaptive IDW decomposition first separates the spatial trends from the local temporal variations. The components are aligned by a newly constructed kernel-based alignment diversity attention (ADA) module. The aligned components andthe raw input data are then adaptively fused using learnable weights. The model training minimizes a newly constructed multi-objectiveAQI-aware loss function, which accounts for the prediction accuracy, the trend preservation, and the alignment with the Air-QualityIndicator (AQI) levels. The numerical experiments were performed for a public dataset of hourly PM2.5 and PM10 data. Assuming oneto three days ahead predictions, the proposed IDW-ADAFormer was found to consistently outperform other existing methods, whilemaintaining the interpretability of an iTransformer.