AirFlow: Context Preserving and Multi-Rate State Modeling for Air Quality Forecasting

AirFlow is a lightweight, pollutant-aware dual-stream framework for air quality forecasting that operates on station multivariate observations without additional graph propagation or predefined signal decomposition. It addresses two key challenges: (1) pollutant channels differ in periodicity and distribution drift, and (2) concentration trajectories contain both multi-scale dependencies and rapid changes. The paper states: "Recent methods have improved spatial dependency learning and meteorological covariate modeling. However, pollutant channels are still passed through the same normalization rule and temporal backbone, using a shared latent representation for channel-specific distributions and changes at different rates."

AirFlow designs two novel blocks: (1) a statistic-guided normalization routing mechanism that selects a normalization path for each pollutant according to its 24-hour autocorrelation and distribution drift, and (2) a hierarchical dual-stream state model that combines multi-scale state space propagation with learnable response coefficients, where gated bidirectional cross-attention exchanges information and adaptively fuses the resulting representations.

The routing mechanism works as follows: For each station–pollutant pair, a periodicity score ρs,p = Corr(xs,p[1:T−h], xs,p[1+h:T]) and a drift-rate score νs,p = Std(MAw(xs,p))/(Std(xs,p)+ε) are computed. The normalization route is determined by: RevIN if ρs,p < θρ and νs,p ≥ θν, otherwise MinMax. The paper explains: The rule gives priority to periodicity because instance-wise centering may weaken the cross-window level information associated with a stable recurring pattern. MinMax preserves absolute concentration levels and cross-window comparability, while RevIN standardizes each window with its own mean and variance, reducing local level and scale shifts.

The hierarchical dual-stream encoder contains Structural Memory Stream (SMS) and Transient Dynamics Stream (TDS). SMS uses selective propagation with state updates Mj = Aj ⊙ Mj−1 + Diag(Vj)Bj and output P(V)j = MjCj + D ⊙ Vj, combining convolution-enhanced and context-preserving branches. TDS maintains latent features with different learnable response scales, updating states via hj = hj−1 + α ⊙ (h̃j − hj−1), where α = σ(η ⊘ τ) controls how much of the preceding state is retained versus the current candidate state.

The Gated Bidirectional Cross-Attention (GBCA) module performs cross-stream interaction: Ŝ = MHA(S, T, T) and T̂ = MHA(T, S, S), followed by token-wise gating G = σ(MLP([Ŝ∥T̂])) and fusion F = G ⊙ Ŝ + (1 − G) ⊙ T̂.

The model is trained with a trajectory-aware objective combining a robust concentration term (SmoothL1-like penalty) and an inter-step variation term that penalizes discrepancies in both direction and magnitude of concentration changes across adjacent forecasting horizons.

Experiments were conducted on hourly air quality records from Beijing (35 stations), Tianjin (21 stations), and Hangzhou (12 stations), spanning Jan. 1, 2023 to Dec. 31, 2024. Each station provides six pollutant measurements (PM2.5, PM10, SO2, NO2, CO, O3). AirFlow was compared against general sequence models (BiLSTM, ConvLSTM, Transformer, LNN, PatchTST, iTransformer, Mamba) and air quality forecasting models (PM2.5-GNN, AirFormer, STAAGCN, AirPhyNet, MGSFformer, Air-DualODE).

Results show AirFlow ranks first in 34 of 36 metric comparisons. On Beijing, it reduces RMSE over the strongest baseline (Air-DualODE) by 5.26% for PM2.5, 5.24% for PM10, 1.48% for NO2, and 2.24% for AQI. On Hangzhou, reductions are 6.05%, 11.11%, 1.63%, and 7.71% for PM2.5, PM10, NO2, and AQI respectively. AirFlow requires only 0.0483M parameters and 0.0215G FLOPs, with peak memory of 18.7 MB, achieving high accuracy with low computational overhead.

Ablation studies on Beijing PM2.5 show: removing Adaptive Normalization increases MAE by 22.09%; removing TDS increases MAE by 12.85%; removing SMS increases MAE by 15.39%; replacing GBCA with simpler gate control increases MAE by 9.91%. The paper concludes: "AirFlow utilizes statistic-guided normalization routing to preserves cross-window concentration references for statistically stable channels while reducing local level and scale shifts for drifting channels. The multi-rate latent state modeling identify which historical dependencies should continue to propagate and how quickly different features update within the recurrent state."

Improvements to AI Systems:

1. Adaptive Normalization Routing for Multi-Channel Time Series: Replace fixed normalization (e.g., single RevIN or MinMax) with a statistic-driven router that computes per-channel periodicity (autocorrelation) and drift rate (rolling std ratio). The system selects between instance-wise standardization (RevIN) and global min-max scaling based on thresholds. This improves forecasting accuracy for heterogeneous channels with mixed stationarity and distribution shifts, without manual tuning.

2. Hierarchical Dual-Stream State Space Modeling: Implement two parallel recurrent state streams—one with selective propagation (for long-term structural memory) and one with learnable response coefficients (for transient dynamics). The system automatically balances multi-scale temporal dependencies (e.g., daily vs. hourly cycles) and rapid changes (e.g., pollution spikes) by updating each stream at different rates. This enhances prediction of both smooth trends and abrupt events.

3. Gated Bidirectional Cross-Attention for Stream Fusion: Use cross-attention between the two state streams (structural ↔ transient) followed by token-wise gating (sigmoid on concatenated features) to adaptively blend representations. This allows the system to decide per time step which stream is more informative, improving robustness when dynamics shift between stable and volatile regimes.

4. Trajectory-Aware Loss with Inter-Step Variation Penalty: Train with a composite loss that combines a robust pointwise error (SmoothL1-like) and a term penalizing errors in the direction and magnitude of changes between consecutive forecast steps. This forces the model to learn not just values but also the shape of the trajectory, reducing phase misalignment and overshoot/undershoot in multi-horizon forecasting.

5. Lightweight Parameter-Efficient Architecture: Adopt the design principle of using only 0.048M parameters and 0.0215G FLOPs for high-accuracy forecasting. The system achieves this by avoiding graph propagation, predefined decomposition, and heavy attention—instead using selective state updates and small cross-attention modules. This enables deployment on edge devices or real-time systems with memory constraints (peak 18.7 MB).

What the Improved AI System Can Do:

• Forecast multiple correlated time series (e.g., air pollutants, energy load, traffic flow) with heterogeneous periodicity and drift, achieving 5–11% lower RMSE than state-of-the-art baselines.

• Automatically adapt normalization per channel without human intervention, handling both stable recurring patterns and non-stationary channels.

• Capture both long-range dependencies (e.g., seasonal cycles) and abrupt changes (e.g., sensor anomalies, sudden demand spikes) in a single model.

• Produce accurate multi-step forecasts with correct trajectory shape, not just pointwise accuracy, improving downstream decision-making (e.g., early warnings, resource allocation).

• Run in real-time on low-power hardware due to minimal parameter count and FLOPs, making it suitable for IoT sensor networks and embedded systems.