The uncertainty prediction of \(\hbox {PM}_{2.5}\) has gained significant attention due to its critical impact on public health and environmental policies. However, existing research faces several limitations. First, current methods struggle to simultaneously capture the complex nonlinear and spatiotemporal characteristics of \(\hbox {PM}_{2.5}\) data. Second, most interval prediction approaches rely on single-objective optimization, making it challenging to balance interval coverage, width, and bias. Third, the majority of prediction models are designed for offline settings, limiting their ability to adapt to real-time, rapidly changing data. To address these challenges, this study proposes a novel interval prediction model based on the lower and upper bound estimation framework. The model features an innovative dual-output spatiotemporal parallel network, MHAGCN-LSTM, which integrates multi-head attention and graph convolutional networks to capture complex spatial interactions. Simultaneously, long short-term memory network is employed to model nonlinear temporal dynamics. This architecture effectively extracts spatiotemporal features and models nonlinear relationships within the data. The proposed model is further enhanced with multi-objective optimization, enabling a balanced trade-off among interval coverage, width, and bias. Experiments on \(\hbox {PM}_{2.5}\) datasets from Shanghai and Hefei, China, demonstrate its superior performance compared to existing methods. Moreover, the model is extended for online prediction, allowing real-time responsiveness to dynamic data and offering a practical tool for \(\hbox {PM}_{2.5}\) forecasting.
