Federated learning (FL) has gained widespread attention for its privacy-preserving and collaborative learning capabilities. Due to significant statistical heterogeneity, traditional FL struggles to generalize a shared model across diverse data domains. Personalized federated learning addresses this issue by dividing the model into a globally shared part and a locally private part, with the local model correcting representation biases introduced by the global model. Nevertheless, locally converged parameters more accurately capture domain-specific knowledge, and current methods overlook the potential benefits of these parameters. To address these limitations, we propose PM-MoE architecture. This architecture integrates a mixture of personalized modules and an energy-based personalized modules denoising, enabling each client to select beneficial personalized parameters from other clients. We applied the PM-MoE architecture to nine recent model-split-based personalized federated learning algorithms, achieving performance improvements with minimal additional training. Extensive experiments on six widely adopted datasets and two heterogeneity settings validate the effectiveness of our approach. The source code is available at https://github.com/dannis97500/PM-MOE.

Nitrogen dioxide (NO2) is a critical air pollutant with significant health and environmental implications, particularly in urban areas where high levels of emissions are prevalent. Accurate nowcasting of ground-level NO2 concentrations is essential for effective air quality management and timely public health interventions. Traditional methods often struggle with balancing the spatial accuracy of ensemble learning models and the temporal forecasting strengths of time-series models like long short-term memory (LSTM) networks. In this study, we propose an improved hybrid framework, GC-LSTM, to nowcast regional ground-level NO2 concentrations on an hourly scale based on satellite-derived NO2 vertical column densities (VCDs), meteorological data, and on-site observations. GC-LSTM integrates the spatial learning capabilities of grained cascade forest (gcForest) with the temporal prediction strengths of LSTM networks, leveraging the strengths of both spatial inference and time-series prediction. This study focuses on the Beijing-Tianjin–Hebei (BTH) region, one of China’s most polluted areas, as a case study. Our results indicate that the GC-LSTM framework performs a strong correlation between predicted and observed ground-level NO2 concentrations, with an$R^{2}$of 0.746 and a mean absolute percentage error (MAPE) of 18.4% at a 1-h prediction interval. Even as the prediction intervals extended to 2 and 3 h, the GC-LSTM consistently outperforms the gcForest model across all evaluated metrics, with$R^{2}$values higher by 0.097 and 0.117, and root mean square error (RMSE) values lower by 0.666 and$1.76~\mu \text {g/m}^{3}$than those nowcasted by using the standalone gcForest model, respectively, highlighting its robustness and adaptability. Furthermore, the capacity of the GC-LSTM framework for continual learning and adaptation ensures its effectiveness in dynamic environments, making it a valuable tool for real-time air quality forecasting and environmental management.