NeuroDDAF: Neural Dynamic Diffusion-Advection Fields with Evidential Fusion for Air Quality Forecasting

Accurate air quality forecasting is crucial for protecting public health and guiding environmental policy, yet it remains challenging due to nonlinear spatiotemporal dynamics, wind-driven transport, and distribution shifts across regions. Physics-based models are interpretable but computationally expensive and often rely on restrictive assumptions, whereas purely data-driven models can be accurate but may lack robustness and calibrated uncertainty. To address these limitations, we propose Neural Dynamic Diffusion-Advection Fields (NeuroDDAF), a physics-informed forecasting framework that unifies neural representation learning with open-system transport modeling. NeuroDDAF integrates (i) a GRU-Graph Attention encoder to capture temporal dynamics and wind-aware spatial interactions, (ii) a Fourier-domain diffusion-advection module with learnable residuals, (iii) a wind-modulated latent Neural ODE to model continuous-time evolution under time-varying connectivity, and (iv) an evidential fusion mechanism that adaptively combines physics-guided and neural forecasts while quantifying uncertainty. Experiments on four urban datasets (Beijing, Shenzhen, Tianjin, and Ancona) across 1-3 day horizons show that NeuroDDAF consistently outperforms strong baselines, including AirPhyNet, achieving up to 9.7% reduction in RMSE and 9.4% reduction in MAE on long-term forecasts. On the Beijing dataset, NeuroDDAF attains an RMSE of 41.63 $μ$g/m$^3$ for 1-day prediction and 48.88 $μ$g/m$^3$ for 3-day prediction, representing the best performance among all compared methods. In addition, NeuroDDAF improves cross-city generalization and yields well-calibrated uncertainty estimates, as confirmed by ensemble variance analysis and case studies under varying wind conditions.

Meteorology-Driven GPT4AP: A Multi-Task Forecasting LLM for Atmospheric Air Pollution in Data-Scarce Settings

Accurate forecasting of air pollution is important for environmental monitoring and policy support, yet data-driven models often suffer from limited generalization in regions with sparse observations. This paper presents Meteorology-Driven GPT for Air Pollution (GPT4AP), a parameter-efficient multi-task forecasting framework based on a pre-trained GPT-2 backbone and Gaussian rank-stabilized low-rank adaptation (rsLoRA). The model freezes the self-attention and feed-forward layers and adapts lightweight positional and output modules, substantially reducing the number of trainable parameters. GPT4AP is evaluated on six real-world air quality monitoring datasets under few-shot, zero-shot, and long-term forecasting settings. In the few-shot regime using 10% of the training data, GPT4AP achieves an average MSE/MAE of 0.686/0.442, outperforming DLinear (0.728/0.530) and ETSformer (0.734/0.505). In zero-shot cross-station transfer, the proposed model attains an average MSE/MAE of 0.529/0.403, demonstrating improved generalization compared with existing baselines. In long-term forecasting with full training data, GPT4AP remains competitive, achieving an average MAE of 0.429, while specialized time-series models show slightly lower errors. These results indicate that GPT4AP provides a data-efficient forecasting approach that performs robustly under limited supervision and domain shift, while maintaining competitive accuracy in data-rich settings.

One-for-All: A Lightweight Stabilized and Parameter-Efficient Pre-trained LLM for Time Series Forecasting

We address the challenge of adapting pre-trained Large Language Models (LLMs) for multivariate time-series analysis, where their deployment is often hindered by prohibitive computational and memory demands. Our solution, One-for-All, introduces Gaussian Rank-Stabilized Low-Rank Adapters (rsLoRA) to enable parameter-efficient fine-tuning of frozen LLMs. While inspired by LoRA, rsLoRA introduces a mathematically grounded rank-stabilization mechanism that enables provable gradient stability at low ranks a novel contribution absent in prior PEFT methods. Our framework injects trainable rank decomposition matrices (rank 16) into positional embeddings and output layers, while keeping self-attention weights fixed. This design reduces trainable parameters by 6.8$\times$ (vs. TimesNet), 21$\times$ (vs. GPT4TS), and 11.8$\times$ (vs. TIME-LLM), while achieving a 168-1,776$\times$ smaller memory footprint (2.2MiB vs. 340MiB-4.18GiB in SOTA models). Rigorous evaluation across six time-series tasks demonstrates that One-for-All achieves state-of-the-art efficiency-accuracy trade-offs: 5.5$\times$ higher parameter efficiency (MSE=5.50) than TimesNet and 21$\times$ better than GPT4TS, while matching their forecasting accuracy (MSE=0.33). The framework's stability is validated through consistent performance across diverse horizons (96-720 steps) and datasets (ETT, Weather, M3, M4), with 98.3% fewer parameters than conventional transformers. These advances enable deployment on edge devices for healthcare, finance, and environmental monitoring without compromising performance.