Cross-Resolution Attention Network for High-Resolution PM2.5 Prediction

Vision Transformers have achieved remarkable success in spatio-temporal prediction, but their scalability remains limited for ultra-high-resolution, continent-scale domains required in real-world environmental monitoring. A single European air-quality map at 1 km resolution comprises 29 million pixels, far beyond the limits of naive self-attention. We introduce CRAN-PM, a dual-branch Vision Transformer that leverages cross-resolution attention to efficiently fuse global meteorological data (25 km) with local high-resolution PM2.5 at the current time (1 km). Instead of including physically driven factors like temperature and topography as input, we further introduce elevation-aware self-attention and wind-guided cross-attention to force the network to learn physically consistent feature representations for PM2.5 forecasting. CRAN-PM is fully trainable and memory-efficient, generating the complete 29-million-pixel European map in 1.8 seconds on a single GPU. Evaluated on daily PM2.5 forecasting throughout Europe in 2022 (362 days, 2,971 European Environment Agency (EEA) stations), it reduces RMSE by 4.7% at T+1 and 10.7% at T+3 compared to the best single-scale baseline, while reducing bias in complex terrain by 36%.

Inverse Neural Operator for ODE Parameter Optimization

We propose the Inverse Neural Operator (INO), a two-stage framework for recovering hidden ODE parameters from sparse, partial observations. In Stage 1, a Conditional Fourier Neural Operator (C-FNO) with cross-attention learns a differentiable surrogate that reconstructs full ODE trajectories from arbitrary sparse inputs, suppressing high-frequency artifacts via spectral regularization. In Stage 2, an Amortized Drifting Model (ADM) learns a kernel-weighted velocity field in parameter space, transporting random parameter initializations toward the ground truth without backpropagating through the surrogate, avoiding the Jacobian instabilities that afflict gradient-based inversion in stiff regimes. Experiments on a real-world stiff atmospheric chemistry benchmark (POLLU, 25 parameters) and a synthetic Gene Regulatory Network (GRN, 40 parameters) show that INO outperforms gradient-based and amortized baselines in parameter recovery accuracy while requiring only 0.23s inference time, a 487x speedup over iterative gradient descent.

TopoFlow: Physics-guided Neural Networks for high-resolution air quality prediction

We propose TopoFlow (Topography-aware pollutant Flow learning), a physics-guided neural network for efficient, high-resolution air quality prediction. To explicitly embed physical processes into the learning framework, we identify two critical factors governing pollutant dynamics: topography and wind direction. Complex terrain can channel, block, and trap pollutants, while wind acts as a primary driver of their transport and dispersion. Building on these insights, TopoFlow leverages a vision transformer architecture with two novel mechanisms: topography-aware attention, which explicitly models terrain-induced flow patterns, and wind-guided patch reordering, which aligns spatial representations with prevailing wind directions. Trained on six years of high-resolution reanalysis data assimilating observations from over 1,400 surface monitoring stations across China, TopoFlow achieves a PM2.5 RMSE of 9.71 ug/m3, representing a 71-80% improvement over operational forecasting systems and a 13% improvement over state-of-the-art AI baselines. Forecast errors remain well below China's 24-hour air quality threshold of 75 ug/m3 (GB 3095-2012), enabling reliable discrimination between clean and polluted conditions. These performance gains are consistent across all four major pollutants and forecast lead times from 12 to 96 hours, demonstrating that principled integration of physical knowledge into neural networks can fundamentally advance air quality prediction.