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

2026 · arxiv_cs

arXiv CS · Papers · 2026

deep-learning machine-learning neural-networks

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

Nan Chen∗

Yijie Dong

Yuchen Zhang

Wei Zhang† School of Software Technology, Zhejiang University Hangzhou, Zhejiang 310000, China

arXiv:2608.09775v1 [cs.AI] 10 Aug 2026

Abstract Accurate air quality forecasting is essential for public health and urban environmental management, but remains challenging because pollutant channels differ in periodicity and distribution drift, while their concentration trajectories contain both multi-scale dependencies and rapid changes. 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. To address this limitation, we propose AirFlow, a pollutant-aware dual-stream framework that operates on station multivariate observations without additional graph propagation or predefined signal decomposition. Specifically, 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. Experiments on real-world data from multiple cities show that AirFlow achieves the best performance in 34 of 36 metrics comparisons, with reductions of up to 11.11% root mean square error over the state-of-the-art baseline. AirFlow also requires only 0.0483M parameters and 0.0215G FLOPs, achieving high forecasting accuracy with low computational overhead.

Introduction

tions. Increasing the complexity of graph propagation therefore does not necessarily resolve the forecasting errors caused by unobserved environmental changes. These unobserved changes manifest in the measured trajectories as abrupt peaks, rapid rises or drops, and shifts in level and variability. Such changes are difficult because a forecasting model must preserve the historical context preceding a pollution episode while responding rapidly once the concentration regime changes. We therefore study a complementary question to increasingly elaborate spatial modeling: how to improve pollutant-aware temporal state evolution when transport context is incomplete. This forecasting scenario poses two related modeling challenges. First, different pollutants exhibit distinct statistical characteristics. PM2.5 and PM10 are more susceptible to local emissions, dust, accumulation, and rapid removal, resulting in abrupt peaks, baseline drift, and non-stationary fluctuations [20]. In contrast, NO2 often shows traffic activity-related periodicity, while O3 presents diurnal variation. Applying a shared normalization strategy may preserve useful magnitude relations

Air pollution remains a major concern for urban environmental management, public health protection, and early warning systems [1, 47]. Fine particulate matter and gaseous pollutants are closely associated with respiratory and cardiovascular diseases [4, 7], while severe pollution episodes increase the burden on healthcare systems and emergency response [23]. Reliable air quality forecasting is therefore essential for proactive risk assessment and policy intervention. Spatial modeling remains valuable when inter-station transport can be supported by synchronized wind fields, emission inventories, terrain attributes, and boundarylayer conditions. In many operational monitoring systems, however, these variables are unavailable, coarsely sampled, or temporally misaligned with pollutant observations [8, 35]. Under this setting, coordinates and historical correlations provide useful but incomplete spatial priors, because the effective influence between stations varies with atmospheric transport and emission condi-

Incomplete Transport Context

Heterogeneous Dynamics

AirFlow Solution

Pollutant-Specific Statistics PM2.5

Peaks & Drift

PM10

Large Fluctuations

NO2

Spatial relations may not reflect time-varying pollutant transport.

Periodic Variations

...

Diurnal Cycle

Entangled Dynamics:

Unavailable, coarse, or misaligned Persistent Context, Periodic Patterns

Wind Emission Boundary Terrain Field Inventory Layer

Sharp Peaks, Rapid Rises/Drops

... Input Multi-Pollutant Sequences Pollutant-Adaptive Normalization Structural Memory Transient Dynamics Gated CrossAttention Fusion

← Stable Events SMS↑

Forecast

→ Abrupt Events TDS↑

Figure 1: Motivation and framework of AirFlow for multivariate air quality forecasting. framework that couples statistic-guided normalizafor some variables while compressing local variations or tion routing with multi-rate latent state modeling. amplifying distribution shifts in others [22, 28]. Second, The routing mechanism preserves cross-window conthe temporal behavior of each pollutant is nonuniform. Periodic activity and gradual accumulation generate percentration references for statistically stable chansistent dependencies [9], whereas changes in emissions, nels while reducing local level and scale shifts for drifting channels, avoiding a uniform preprocessing dispersion, and removal conditions produce sharp rises, assumption across pollutants. rapid drops, and short-lived peaks [3, 27]. Accurate forecasting therefore requires both stable historical context • We design a novel hierarchical dual stream state and flexible responses to changing concentration condimodel that combines multi-scale dependency modtions [12, 15]. Figure 1 summarizes the forecasting sceeling with heterogeneous hidden state transitions. nario, the modeling challenges, and the overall design of Gated bidirectional cross-attention conditions rapidAirFlow. response features on relevant historical context beExisting forecasting methods address these difficulfore adaptive fusion. ties only partially [24]. General sequence models usually process all pollutants using shared normalization • Experiments across multiple cities and pollutants and single state-update mechanism, limiting their ability show accuracy gains and competitive computational to accommodate variable-specific statistics and nonunioverhead without additional graph propagation. form changes [48]. Decomposition-based methods separate sequences into trend, seasonal, frequency, or multiscale components [40], but their predefined or shared 2 Related Work decomposition bases may not adapt well to pollutant concentration distributions, while component-wise pro2.1 Air Quality Forecasting cessing may represent abrupt variations as residual or high-frequency parts without sufficiently preserving their Spatial inductive biases are widely adopted in air-quality connection to the preceding pollution state. These limforecasting to represent interactions across monitoring itations motivate an adaptive framework that accomlocations. PM2.5 -GNN incorporates geographical knowlmodates pollutant-specific distributions while combining edge into graph construction, whereas GAGNN models contextual dependency modeling with state transitions. dependencies at both city and city-group levels [2, 38]. AirFlow addresses air quality forecasting under inAirFormer develops scalable spatial attention for timecomplete transport context by coordinating two levels of varying correlations over a nationwide monitoring netpollutant heterogeneity: statistic-guided normalization work [25]. DGN-AEA further constructs dynamic relapreserves channel-dependent distribution information, while tions from adaptive edge attributes [44], while DSGT complementary state-transition pathways model persisconstructs them from time-varying station observations tent context and heterogeneous response rates without and auxiliary features [42]. MGSFformer combines multipredefined decomposition or graph propagation. The main granularity observations with spatiotemporal correlations contributions of this work are summarized as follows: [46]. These methods improve spatial representation through increasingly flexible relation construction, while the learned

• We propose AirFlow, a lightweight pollutant-aware 2

Linear

MinMax Router

Input

Gated

B×L×P

HDS-1

HDS-2

HDS-3

Decoder

Output B×O

RevIN

DSFE

Adaptive Normalization

DSFF

Hierarchical Dual Stream

Dual Stream Feature Extraction（DSFE）

Dual Stream Feature Fusion（DSFF）

B×L×d B×L×d

Linear

Structural Memory Stream S Transient Dynamics Stream T

B×d

DWConv1D

SiLU

MHA(Q=S,K=T,V=T)

SiLU Selective

Propagation

𝒫

Selective

Propagation

𝒫

MHA(Q=T,K=S,V=S) ^ T

^ S …

Neurons

Gated Fusion

^ + (1 − G) ⊙ T ^ F = G ⊙S

Linear Feed Forward Transformation

Linear B×L×d

B×L×d

HK Structural Memory Stream

Transient Dynamics Stream

Figure 2: Overall architecture of AirFlow. Adaptive Normalization handles heterogeneous statistics via statisticguided router. Stacked Hierarchical Dual Stream (HDS) composed of Dual Stream Feature Extraction (DSFE) and Dual Stream Feature Fusion (DSFF). DSFE learns complementary representations through Structural Memory Stream and Transient Dynamics Stream, while DSFF fuses them via gated cross-attention. The final representations are decoded for forecasting. dependencies remain tied to the signals used to infer inter-station relations. Beyond learned spatial relations, recent studies incorporate atmospheric knowledge into the forecasting process. MasterGNN processes air quality and weather stations modeling and suppresses observation noise accumulation caused by spatial-temporal propagation [13]. CauAir models the causal association between weather covariates and Air Quality Index (AQI) [31]. Physicsguided methods further encode transport dynamics. AirPhyNet represents diffusion and advection with graphbased differential equation networks, Air-DualODE combines open system physical dynamics with a data-driven Neural ordinary differential equation (ODE) branch, and AirDDE models propagation delays through multifactor historical features and delay function grounded in diffusion and advection processes [18, 36, 39]. These studies demonstrate that spatial and meteorological context provides valuable information for air quality forecasting. However, recent advances have emphasized sophisticated spatial dependency modeling, while the heterogeneous temporal patterns of pollutant concentrations

remain underexplored. Additional spatial dependencies enrich contextual information, but they may also compensate for, rather than resolve, insufficient modeling of abrupt changes and non-stationary patterns. This motivates us to strengthen pollutant-aware temporal modeling and verify whether competitive or better performance can be achieved without constructing additional graph propagation.

2.2

Normalization and Temporal Modeling

Normalization methods address non-stationarity by controlling which statistics are removed, estimated, and restored. Reversible Instance Normalization (RevIN) applies reversible instance mean and variance normalization, whereas SAN estimates evolving statistics over local temporal slices [22, 30]. SIN selects statistics according to local invariance and global variability [14]; FAN and DDN extend normalization to frequency-domain and dual-domain distribution changes [5, 45]. These methods show that normalization choices embody different as3

sumptions about distribution change, motivating pollutantwise routing rather than one fixed operator across channels. Temporal forecasting models capture sequence dependencies through different computational mechanisms. Convolutional neural network (CNN)-based models extract local patterns with temporal convolutions, whereas recurrent neural network (RNN)-based models propagate historical information through recurrent hidden states [41]. Transformer-based models capture long-term interactions with attention [48], while selective state space models provide input-dependent state propagation with linear sequence complexity [6, 11]. Liquid neural network (LNN)-based models regulate hidden-state transitions through differential dynamics [15, 16]. To address non-stationarity and temporal patterns at different scales, recent models further introduce adaptive decomposition, multi-resolution processing, and frequencydomain representations [17, 19, 21, 43]. These works suggest that component construction and latent-state modeling are complementary design strategies. AirFlow follows the latter to model multi-scale context and ratevarying changes without relying on a fixed component partition.

3.2

Station-Wise Pollutant Normalization

For pollutant p at station s, let xs,p ∈ RT denote its training sequence, where T is the sequence length. The periodicity score is ρs,p = Corr (xs,p [1:T − h], xs,p [1 + h:T ]) ,

(2)

where h is the lag of one diurnal cycle and Corr denotes the Pearson correlation coefficient [33]. The driftrate score is Std (MAw (xs,p )) , (3) νs,p = Std(xs,p ) + ε where MAw is the moving average with weekly window length w, Std denotes standard deviation, and ε > 0 prevents division by zero. The score νs,p summarizes the relative variation of the smoothed sequence. The normalization route is determined for each station– pollutant pair: ( RevIN, ρs,p < θρ ∧ νs,p ≥ θν , (4) rs,p = MinMax, otherwise,

where θρ and θν are routing thresholds. The rule gives priority to periodicity because instance-wise centering may weaken the cross-window level information associated with a stable recurring pattern. For input window i from station s, let xs,i,p ∈ RL 3 Methodology denote pollutant p. Its normalized sequence is  xs,i,p − xmin,s,p   , rs,p = MinMax, 3.1 Problem Formulation  x max,s,p − xmin,s,p + ε es,i,p = x xs,i,p − µs,i,p Let S denote the set of monitoring stations. For station   + βp , rs,p = RevIN,  γp L×P s ∈ S and forecasting origin t, the input Xs,t ∈ R σs,i,p contains L observations of P pollutants collected at the (5) same station. For a fixed target pollutant, AirFlow learns where xmin,s,p and xmax,s,p are the station training extrema, µs,i,p and σs,i,p are the mean and standard devibs,t = f (Xs,t ; Θ) ∈ RO , y (1) ation of the input window, γp and βp are learnable affine parameters. MinMax uses the station-specific training where O is the forecasting horizon and Θ denotes the range for every input window, preserving absolute conmodel parameters. Training sequences are generated by centration levels and cross-window comparability. RevIN sliding a window over each station, and the model is standardizes each window with its own mean and varishared across all stations. The target pollutant is fixed ance, reducing local level and scale shifts [22]. AirFlow in each training run. prefers MinMax when a stable periodic pattern provides AirFlow is designed for two properties of multi-pollutant a reliable cross-window reference, and uses RevIN when observations. Pollutants differ in periodicity and distriweak periodicity is accompanied by stronger slow distribution shift, making a single normalization rule unsuitbution movement. The normalized channels are concateable for all channels. Their trajectories also contain longnated and projected to the initial hidden representation range dependencies and rapid variations that favor difH0 ∈ Rn×L×d , where n is the batch size and d is the ferent state-update patterns. AirFlow therefore combines hidden dimension. The corresponding target statistics station pollutant normalization with two temporal streams. are retained for inverse transformation. As shown in Figure 2, the normalized sequence is projected to a d-dimensional latent space and passed through 3.3 Hierarchical Dual-Stream Encoder K Hierarchical Dual-Stream (HDS) blocks. Each block contains Structural Memory Stream (SMS), Transient AirFlow stacks K residual HDS blocks to refine the laDynamics Stream(TDS), and Gated Bidirectional Crosstent representation. Let Hk denote the input to the k-th Attention (GBCA) module. A prediction head maps the block, with H0 produced by the input projection and final representation to the future target sequence. k = 0, . . . , K − 1. 4

3.3.1

Structural Memory Stream

3.3.3

A learned projection of Hk produces two representations. The convolution-enhanced representation is U = SiLU(DWConv(Πu (Hk ))), and the context-preserving representation is Z = SiLU(Πz (Hk )), where Πu and Πz are learned projections and DWConv is depth-wise temporal convolution. The selective propagation operator P is applied to both representations, that is U′ = P(U) and Z′ = P(Z). To define the operator, let V ∈ {U, Z} denote either input representation. The input at position j generates a positive discretization vector ∆j ∈ Rde and vectors Bj , Cj ∈ Rds , where de is the expanded width and ds is the state dimension. Let A ∈ Rde ×ds denote the transition coefficients, with A = − exp(Alog ). We define Aj = exp(Diag(∆j )A) and Bj = ∆j B⊤ j . The state Mj ∈ Rde ×ds is updated by Mj = Aj ⊙ Mj−1 + Diag(Vj )Bj ,

(6)

b = MHA(T, S, S), T

(10)

where the arguments of Multi-Head Attention (MHA) are query, key, and value [37]. This bidirectional retrieval allows each stream to be conditioned on the other before their relative contributions are estimated by the tokenb T])), b wise gate G = σ(MLP([S∥ where ∥ denotes concatenation. The fused representation is b + (1 − G) ⊙ T. b F=G⊙S

3.4

(11)

Prediction

After the final HDS block, the representation is decoded by mean pooling and two-layer prediction head D:   L X 1 b = D HK,j  . (13) y L j=1

(8)

where Wo projects the expanded representation back to width d. The symmetric interaction combines local filtering with selective propagation without introducing a predefined decomposition. 3.3.2

b = MHA(S, T, T), S

where Φ denotes the feed forward transformation applied after fusion.

(7)

where D ∈ Rde is the direct term. The product Mj Cj is matrix–vector multiplication. The symbols A, B, C, and D follow the standard state-space roles [6, 11]. The SMS output is S = Wo [U′ ⊙ Z + Z′ ⊙ U] ,

The GBCA module performs cross-stream interaction and adaptive fusion. Specifically, the SMS representation uses the TDS representation as key and value to retrieve recurrent state information, while the reverse direction retrieves propagated context information:

The gate is estimated at each temporal position from the mutually conditioned representations. The block output is Hk+1 = Hk + Φ(F), (12)

where Diag(·) forms a diagonal matrix and ⊙ denotes element-wise multiplication. The propagated output is P(V)j = Mj Cj + D ⊙ Vj ,

Gated Bidirectional Cross-Attention

Training is performed in the scale associated with the target route, and predictions are transformed back to the original concentration scale for evaluation. Multi-step air quality forecasting requires both accurate concentration values and consistent changes across adjacent forecasting horizons. We therefore optimize a trajectory-aware objective with a robust concentration term and an inter-step variation term:

Transient Dynamics Stream

TDS maintains a set of latent features with different learnable response scales. At position j, the candidate e j = tanh(Wx Hk,j +Wh hj−1 +bh ), its response state is h coefficients are computed as α = σ(η ⊘ τ ), where η is learnable scalar, τ is learnable vector, ⊘ is element-wise division, and σ is sigmoid function. The state is updated by e j − hj−1 ). hj = hj−1 + α ⊙ (h (9)

1 XX ψ(ei,o ) + λ∆ L∆ , nO i=1 o=1

(14)

where ei,o = ybi,o −yi,o is the point-wise forecasting error, and λ∆ controls the variation term. The penalty ψ is:  e2  λs + λ1 |e|, |e| < κ, 2κ ψ(e) = (15)  (λ + λ )|e| − λs κ , |e| ≥ κ, s 1 2

Different latent features require different degrees of temporal persistence, some need to accumulate information over longer contexts, whereas others need to respond more rapidly to recent observations. A smaller entry of α retains more of the preceding state, while a larger entry places greater weight on the current candidate state. Finally, the recurrent states are projected to obtain T ∈ Rn×L×d .

where κ > 0 is the transition point and λs , λ1 ≥ 0 are fixed weights. This penalty retains quadratic sensitivity to small residuals and grows linearly for large residuals, 5

preventing a small number of severe pollution episodes from dominating optimization while maintaining a direct penalty on absolute concentration deviations. Point-wise accuracy does not constrain how the predicted trajectory changes across horizons. The inter-step variation term is L∆ =

n O−1 X X 1 2 (∆b yi,o − ∆yi,o ) , n(O − 1) i=1 o=1

exhibit limited performance. Although Mamba improves computational efficiency, it does not outperform recurrent baselines. The vanilla Transformer underperforms due to the lack of temporal inductive bias, whereas its variants (e.g., iTransformer and PatchTST) achieve better results by augmenting variable-wise dependencies or local temporal representation. LNN has relatively fewer neurons but is originally developed for causal decisionmaking under irregular sampling, thus failing to achieve competitive performance on this task. In contrast, domain-specific models designed for spatiotemporal air quality forecasting exhibit clear advantages over general-purpose sequence models. Especially the physics-guided model Air-DualODE retains RMSE advantage on Tianjin PM2.5 and AQI. It is also worth noting that on the NO2 forecasting task, where temporal fluctuations are driven by regular anthropogenic activities, the performance differences among most models remain relatively small. AirFlow ranks first in 34 of the 36 comparisons while operating only on station-level multivariate observations. On the Beijing dataset, 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 the Hangzhou dataset, which represents a different geographic domain characterized by subtropical monsoon climate and hightech manufacturing emissions, AirFlow reduces RMSE over the Air-DualODE by 6.05%, 11.11%, 1.63%, and 7.71% for PM2.5 , PM10 , NO2 , and AQI. These results indicate that in pollutant-only scenarios, prioritizing station pollutant dynamics can achieve strong forecasting accuracy without additional graph propagation.

(16)

where ∆b yi,o = ybi,o+1 − ybi,o and ∆yi,o = yi,o+1 −yi,o . This design couples adjacent forecasting horizons and penalizes discrepancies in both the direction and magnitude of concentration changes.

Experiments

4.1

Experimental Settings

Datasets We evaluate AirFlow on hourly air quality records from Beijing, Tianjin, and Hangzhou. All datasets are publicly available at https://quotsoft.net/air. After filtering stations with PM2.5 missing rates below 20%, the three datasets contain 35, 21, and 12 monitoring stations. Each dataset spans from Jan. 1, 2023 to Dec. 31, 2024. The data from each station are divided chronologically into training, validation, and test sets with a ratio of 8:1:1. Each station provides six pollutant measurements, including PM2.5 , PM10 , SO2 , NO2 , CO, and O3 . The four forecasting targets are listed in Table 1. PM2.5 is treated as the primary forecasting target due to its critical health impacts. Baselines We compare AirFlow with general sequence models and air quality forecasting models. The former includes BiLSTM [10], ConvLSTM [34], Transformer [37], LNN [15], PatchTST [32], iTransformer [29], and Mamba [11], covering recurrent, convolutional, attention-based, and state-space architectures. The latter includes PM2.5GNN [38], AirFormer [25], STAAGCN [26], AirPhyNet [18], MGSFformer [46], and Air-DualODE [36], which introduce spatial dependency learning, atmospheric priors, or auxiliary environmental context. Metrics Forecasts are evaluated in the original concentration scale using root mean square error (RMSE), Mean Absolute Error (MAE), and Coefficient of Determination (R2 ). These metrics quantify the model’s error magnitude, overall accuracy, and goodness of fit.

4.2

4.3

Ablation Study

To evaluate the contribution of components in AirFlow, we conduct ablation studies on the Beijing PM2.5 task. As shown in Table 2, AirFlow achieves the best performance across all evaluation metrics, demonstrating that each component contributes positively to the final performance. V0 removes AN, i.e. uses fixed MinMax, leads to 22.09% increase in MAE and 4.89% decrease in R2 , showing that input representation is sensitive to which station-level statistics are retained before temporal encoding. Removing TDS (V3 ) increases MAE by 12.85%, while removing SMS (V4 ) leads to a larger increase of 15.39%. These results indicate that modeling either long-term temporal correlations or abrupt change patterns is insufficient to match the performance of the full model. Within SMS, removing the context-preserving branch (V5 ) increases MAE by 7.23%, while removing the convolution-enhanced branch (V6 ) leads to 6.29% increase. Replacing GBCA with a simpler gate control (V7 ) increases MAE by 9.91% and reduces R2 by 2.1% relative to the AirFlow, indicating that fine-grained feature in-

Main Results

To demonstrate the effectiveness and robustness of AirFlow, we compared its performance with various stateof-the-art baselines. For fair comparisons, all baselines and AirFlow are evaluated under an identical experimental setup. As shown in Table 1, several interesting observations can be drawn. General-purpose sequence models 6

Table 1: Experimental results comparing AirFlow with baseline models across four target variables, averaged over three runs. Lower RMSE and MAE and higher R2 indicate better performance. Best results are highlighted in bold. Dataset

Model

PM2.5

PM10

NO2

AQI

RMSE ↓

MAE ↓

R2 ↑

RMSE ↓

MAE ↓

R2 ↑

RMSE ↓

MAE ↓

R2 ↑

RMSE ↓

MAE ↓

R2 ↑

Beijing

BiLSTM (2014) ConvLSTM (2015) Transformer (2017) PM2.5-GNN (2020) LNN (2021) PatchTST (2023) AirFormer (2023) STAAGCN (2023) iTransformer (2024) Mamba (2024) AirPhyNet (2024) MGSFformer (2025) Air-DualODE (2025) AirFlow (Ours)

16.44 16.48 17.33 15.84 17.02 16.12 15.68 15.98 15.88 16.64 15.93 15.62 15.22 14.42

9.01 9.08 10.34 8.42 8.67 8.83 8.40 8.41 8.58 8.62 8.87 8.29 8.18 7.47

0.8113 0.8104 0.7903 0.8262 0.7978 0.8186 0.8284 0.8132 0.8239 0.8068 0.8127 0.8297 0.8348 0.8513

28.89 30.51 27.13 24.85 26.10 30.29 26.45 24.81 29.89 26.19 33.18 25.42 23.67 22.43

15.06 15.41 16.18 13.88 14.29 14.03 13.96 13.90 13.92 14.46 18.32 14.12 13.38 13.02

0.7451 0.7157 0.7751 0.8182 0.7919 0.7197 0.7862 0.8120 0.7270 0.7904 0.7002 0.8098 0.8310 0.8443

12.79 12.76 12.80 12.82 12.83 12.75 12.79 12.82 12.95 12.81 14.17 12.76 12.84 12.65

8.68 8.70 8.58 8.89 8.59 8.59 8.61 8.72 8.78 8.64 9.71 8.60 8.88 8.55

0.6823 0.6835 0.6814 0.6788 0.6803 0.6872 0.6815 0.6806 0.6742 0.6814 0.5915 0.6822 0.6794 0.6889

22.14 21.46 21.16 20.12 21.73 20.09 21.60 20.29 20.95 22.09 20.49 20.32 19.68 19.24

12.08 12.12 11.83 11.44 11.75 11.43 11.30 11.48 11.46 11.99 11.49 11.39 11.21 10.87

0.7616 0.7761 0.7854 0.8096 0.7703 0.7937 0.7730 0.7999 0.7866 0.7626 0.8088 0.8007 0.8108 0.8184

Tianjin

20.09 19.95 21.67 19.22 20.06 19.63 20.39 19.87 19.58 19.82 20.18 19.70 18.78 18.87

11.91 11.86 13.08 11.45 11.70 11.78 11.89 11.66 11.79 11.68 12.07 11.54 10.98 10.97

0.6828 0.6867 0.6311 0.6897 0.6839 0.6988 0.6734 0.6897 0.6921 0.6913 0.6799 0.6966 0.6974 0.7124

28.26 28.46 30.02 27.88 29.19 28.08 28.43 29.04 28.40 29.31 29.98 27.89 27.65 26.87

17.81 18.40 19.49 17.12 18.34 17.28 17.49 18.35 17.91 18.54 18.98 17.11 16.87 16.81

0.6717 0.6670 0.6296 0.6945 0.6497 0.6760 0.6678 0.6533 0.6685 0.6468 0.6305 0.6859 0.7001 0.7046

14.79 14.71 14.96 14.98 14.78 14.66 14.59 14.85 14.61 15.05 15.23 14.63 15.11 14.54

9.87 10.04 9.91 10.01 9.82 9.85 9.86 10.09 9.82 10.11 11.76 9.88 10.44 9.78

0.6681 0.6716 0.6601 0.6623 0.6687 0.6739 0.6767 0.6653 0.6762 0.6563 0.6488 0.6772 0.6537 0.6793

24.12 23.74 24.39 23.02 24.07 23.44 23.38 24.02 24.69 24.39 23.88 23.06 22.51 22.58

14.85 14.62 14.73 13.98 14.47 13.91 14.02 14.45 14.77 14.83 14.58 14.01 13.52 13.48

0.6670 0.6774 0.6595 0.6874 0.6683 0.6856 0.6871 0.6692 0.6510 0.6595 0.6735 0.6908 0.7012 0.7023

Hangzhou

13.34 13.96 15.96 15.23 14.22 16.36 17.78 16.69 17.04 13.01 16.89 17.00 13.22 12.42

8.02 8.75 8.92 9.86 8.83 10.47 10.43 10.92 11.01 8.11 11.76 10.43 8.04 7.28

0.6865 0.6831 0.5654 0.6211 0.6802 0.5439 0.5075 0.5255 0.5053 0.7012 0.5675 0.5075 0.7026 0.7455

18.45 18.51 19.77 18.44 19.44 22.92 24.57 24.74 23.71 18.43 19.04 24.08 18.99 16.88

11.72 11.76 12.17 10.98 12.32 14.96 15.20 16.45 15.63 11.32 11.95 15.40 12.02 10.56

0.6817 0.6789 0.6345 0.6812 0.6468 0.5109 0.4356 0.4300 0.4768 0.6826 0.6609 0.4580 0.6629 0.7224

11.33 11.69 11.28 11.54 11.12 13.16 14.39 13.78 14.03 11.04 12.62 14.55 11.03 10.85

7.92 8.22 7.94 8.18 7.76 9.35 10.13 10.26 9.62 7.68 8.67 10.31 7.91 7.43

0.6107 0.5855 0.6146 0.6001 0.6249 0.4729 0.3710 0.4227 0.4009 0.6304 0.5165 0.3575 0.6306 0.6453

16.64 16.09 17.34 17.45 17.12 20.05 22.95 20.54 21.27 16.47 15.80 20.91 16.08 14.84

9.94 9.98 10.37 10.32 10.45 12.78 13.59 13.85 13.65 9.89 9.76 13.15 10.06 9.02

0.6546 0.6769 0.6246 0.6311 0.6341 0.5001 0.3435 0.4758 0.4378 0.6613 0.6891 0.4551 0.6780 0.7105

teractions are more effective than coarse weighting for multi-scale feature fusion.

Table 2: Ablation study on model components. ! and # indicate whether a module is included or removed. AN: Adaptive Normalization; CE: Convolution-Enhanced Branch in SMS; CP: Context-Preserving Branch in SMS. TDS: Transient Dynamics Stream; GBCA: Cross Attention. Best results are in bold.

4.4

For real-world air quality early-warning systems, computational complexity and memory footprint are as critical as forecasting accuracy. As summarized in Figure 3, AirFlow achieves a superior balance between modeling complexity and computational feasibility. Specifically, its parameter count (0.0483M) is lightweight compared to sequence models like iTransformer (1.6010M), and its FLOPs are approximately 1/95 of the spatiotemporal baseline AirFormer (0.0215G vs. 2.0378G). Furthermore, AirFlow maintains a remarkably low peak memory footprint (18.7 MB), avoiding the exorbitant memory costs of spatial models like MGSFformer (137.7 MB).

Variant AN CE CP TDS GBCA RMSE ↓ MAE ↓ R2 ↑ V0 V1 V2 V3 V4 V5 V6 V7 AirFlow

16.68 16.64 16.81 15.65 15.85 15.46 15.33 15.45 14.42

Computational Efficiency

9.12 0.8097 8.62 0.8068 8.70 0.8026 8.43 0.8276 8.62 0.8201 8.01 0.8323 7.94 0.8359 8.21 0.8334 7.47 0.8513

latent state modeling identify which historical dependencies should continue to propagate and how quickly different features update within the recurrent state. Gated cross-attention enables fine-grained interaction between the two streams, allowing rapid concentration changes to be interpreted against the relevant historical context before producing an integrated forecasting representation. Extensive experiments on three real-world datasets across multiple cities and pollutants demonstrate that AirFlow can provide accurate and efficient air quality forecasting.

0$(302.5

3DUDPV0

Acknowledgements

This work was supported by Deep Earth Probe and Mineral Resources Exploration - National Science and Technology Major Project (2025ZD1007008).

0$(302.5

)/23V*

Figure 3: Computational efficiency comparison based on parameters (upper panel) and FLOPs (lower panel). Bubble size reflects peak memory usage. MAE is reported on the Beijing PM2.5 forecasting task.

Limitations and Future Work

Although AirFlow effectively captures the multi-scale temporal evolution of air quality data through variableadaptive normalization and hierarchical dual-stream architecture, this study is currently constrained by the limited external covariates available in the datasets. Therefore, the potential intervention mechanisms of cross-modal factors on the underlying dynamics have not yet been fully explored. In the future, we expect to extend our research to urban sensing scenarios supported by multisource heterogeneous big data. We aim to investigate how to integrate physical priors with multi-modal features, thereby further enhancing the model’s reasoning capabilities within complex urban atmospheric systems.

Conclusion

In this paper, we propose AirFlow, a lightweight pollutantaware forecasting framework under incomplete transport context. 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

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Appendix

A.1

Experimental Protocol and Reproducibility

A.2

Normalization Routing Analysis We compare fixed normalization with statistic-guided routing to determine whether the gain arises from the normalization operator itself or from pollutant-dependent assignments. The statistics used for routing are computed only from the training split. The thresholds are selected on the validation split and fixed to (θρ , θν ) = (0.425, 0.40) for test evaluation. As shown in Table 5, RevIN provides a strong baseline, while the selected routing configuration yields a further improvement. This result suggests that removing window level and scale shifts is beneficial for most nonstationary sequences, but applying the same transformation to every pollutants may discard useful concentration references. The routing rule retains these references only when the training statistics indicate sufficiently stable periodicity or limited drift. The threshold pairs do not produce a monotonic performance trend. A small threshold change may leave most assignments unchanged or switch several pollutants located near a decision boundary. Figure 5 further illustrates that station–pollutant pairs occupy different regions of the periodicity or drift space, including multiple observations close to the selected boundaries. Spatial Augmentation Analysis To investigate whether introducing spatial inductive biases might lead to a mismatch in the absence of reliable transport priors, we explored several spatial modeling strategies. (1) Spatial Loss: Adding a penalty term to encourage forecasting consistency between proximal stations; (2) Coordinate Embedding: Incorporating station latitude and longitude as additional input features; (3) GCN Fusion: Introducing Graph Convolutional Network (GCN) after the dualstream fusion to aggregate neighborhood information. The results in Table 6 show that the examined spatial augmentations do not yield useful gains under the current coverage. This suggests that, under limited station observations and incomplete transport-related priors, increasing spatial modeling complexity may introduce additional dependencies without addressing abrupt temporal changes in pollutant trajectories. These results motivate us to reconsider whether reliable forecasting can be achieved by modeling station-level pollutant evolution without relying on additional spatial graph propagation.

Datasets Statistics and Station Coverage Statistical summaries of the Beijing, Tianjin and Hangzhou datasets are reported in Table 3, while the spatial distribution of monitoring stations is shown in Figure 4. Table 3: Statistical information of air quality datasets for Beijing, Tianjin, and Hangzhou. Dataset

Pollutant

Unit

Mean

Std.

Beijing

PM2.5 PM10 SO2 NO2 CO O3 AQI

µg/m µg/m3 µg/m3 µg/m3 mg/m3 µg/m3 -

32.69 66.00 2.82 24.57 0.5 64.23 61.23

34.38 85.71 2.11 20.62 0.3 49.52 51.23

Tianjin

PM2.5 PM10 SO2 NO2 CO O3 AQI

µg/m3 µg/m3 µg/m3 µg/m3 mg/m3 µg/m3 -

40.91 78.86 7.36 33.66 0.69 72.04 72.31

40.45 80.78 4.60 24.12 0.38 53.66 54.51

Hangzhou

PM2.5 PM10 SO2 NO2 CO O3 AQI

µg/m3 µg/m3 µg/m3 µg/m3 mg/m3 µg/m3 -

30.76 51.12 6.43 28.93 0.66 62.99 51.91

25.89 39.93 1.92 19.35 0.19 46.26 33.05

Mechanism and Design Analysis

Implementation Details and Hyperparameters All experiments were conducted on two NVIDIA RTX A5000 GPUs (24 GB VRAM) hosted on workstations equipped with Intel Core i7-14700KF CPUs. The software environment comprised Python 3.8.20, PyTorch 2.2.2, and Forecasting Horizon Analysis CUDA 12.1. All baselines are evaluated using the same To validate the robustness of AirFlow under differpollutant variables, historical input windows, target seent input lengths and forecasting horizons, we compared quences, station set, and chronological train/validation/test it with baselines on the Beijing PM2.5 forecasting task. splits. For baselines that model spatial relationships, we As shown in Table 7, although extending the prediction additionally provide the latitude and longitude of each horizon from 6h to 12h increases the errors of all models, monitoring station. The hyperparameter configurations AirFlow retains the good performance, reducing 6.06% are summarized in Table 4. MAE than the state-of-the-art baseline. When fixing the forecasting horizon at 12h, increas12

(a) Beijing (Map)

(b) Tianjin (Map)

(d) Beijing (Satellite)

(e) Tianjin (Satellite)

(f) Hangzhou (Satellite)

Figure 4: Geographical distribution of air quality monitoring stations in Beijing, Tianjin, and Hangzhou. The first row (a)-(c) displays the map views, while the second row (d)-(f) presents the corresponding satellite imagery. Red dots represent the specific deployment locations of the stations. Table 4: Key hyperparameter settings of AirFlow. Config

Description

Values

Optimizer Learning rate scheduler Learning rate Weight decay Multi-head num Number of layers Dropout Batch size Epoch Periodicity threshold Drift-rate threshold Diurnal lag Drift window Hidden dimension Expanded dimension State dimension DWConv kernel size Discretization rank Prediction-head width TDS hidden dimension Step-scale initialization Concentration loss weights Variation loss weight Robust transition point

The algorithm used for parameter optimization. The strategy for adjusting the learning rate during training. The starting value for the learning rate. The L2 regularization coefficient to prevent overfitting. The number of parallel attention mechanisms in the multi-head attention layer. The number of stacked HDS layers in the model. The probability of randomly dropping out units during training. The number of training samples processed per iteration. The total number of complete passes through the training dataset. θρ in the normalization routing rule. θν in the normalization routing rule. Lag h used to compute the periodicity score. Moving-average window w used to compute the drift-rate score. Latent representation width d used throughout the HDS blocks. Expanded width de used in the SMS. State dimension ds of the selective propagation operator. Kernel size of the depth-wise temporal convolution in the SMS. Rank of the projection used to parameterize the discretization vector in the SMS. Hidden width of the two-layer prediction head. Hidden-state width dr of the TDS. Initial value of the learnable scalar η controlling the response coefficients. Weights λs and λ1 of the SmoothL1 and absolute error terms. Weight λ∆ of the inter-step variation loss. Transition point κ of the SmoothL1 penalty

AdamW SGDR 0.0002 0.0001 4 3 0.1 32 60 0.425 0.4 24 168 32 64 16 4 4 16 16 0.1 0.8, 0.15 0.05 1.0

Table 5: Comparison of fixed normalization strategies and statistic-guided routing under different candidate threshold. Strategy

θρ

θν

All MinMax All RevIN

– –

RMSE ↓ MAE ↓

0.425 0.50 0.425 0.45 Statistic-guided 0.425 0.40 Routing 0.400 0.50 0.400 0.45 0.400 0.40 302.5

3010

622

9.12 7.61

0.8097 0.8457

16.12 14.79 14.42 16.54 15.48 15.76

8.98 7.75 7.47 9.04 8.33 8.49

0.8143 0.8412 0.8513 0.8111 0.8301 0.8217

122

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Generalization Analysis

Cross-Period Case Study To evaluate temporal generalization under distribution shifts, we test AirFlow on two non-overlapping periods: Oct. 20–Dec. 31, 2024 and Jan. 1–Sep. 30, 2025. The 2025 records are used only as an additional out-of-period test set. As summarized in Table 8, the later period exhibits a distinct data distribution, with lower average pollution levels but substantially larger extreme values, consistent with changes in meteorological and emission conditions. Table 9 shows that AirFlow maintains stable predictive performance across the two periods. The relative degradation in R2 ranges from 6.07% to 11.19% in Beijing and from 4.74% to 7.99% in Tianjin. In Hangzhou, the degradation for PM2.5 , PM10 , and AQI ranges from 1.99% to 11.04%, while NO2 exhibits a slight improvement. These results indicate that AirFlow remains effective under substantial cross-period distribution changes. The cross-pollutant results further reveal different levels of temporal stability. NO2 is relatively stable across cities, which is consistent with its more regular activityrelated emission patterns, whereas PM10 undergoes larger performance degradation because it is more sensitive to changing dust, transport, and removal conditions. Figure 7 provides representative forecasting trajectories. AirFlow captures abrupt surge-and-drop patterns in particulate matter, including the event around Nov. 2, 2024, while preserving the preceding concentration context. During the summer of 2025, it continues to follow the overall trajectory under frequent short-term fluctuations. Cross-City Transfer Learning A primary challenge in air quality forecasting lies in the diversity of geographical topologies, climatic conditions, and emission structures across cities. By modeling intrinsic multi-scale dependencies and temporal evolution rates, AirFlow capture universal atmospheric dynamics beyond specific regions. To further leverage this property, we adopt a cross-city transfer learning (TL) strategy, where the model is initialized with pre-trained weights from Beijing and finetuned on two target domains: Tianjin (physically proximate) and Hangzhou (geographically distant with distinct emission profiles). As shown in Table 10, TL strategy yields improvements in Tianjin, suggesting that the model transfers shared regional transport dynamics and background atmospheric states within geographically proximate areas. This improvement indicates that the learned representations encode not only local correlations but also physically meaningful cross-city dependencies. In contrast, in Hangzhou, the model still maintains competitive performance across major pollutants, implying that the captured temporal evolution patterns are invariant to regional differences. The relatively slight variation observed

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R2 ↑

16.68 14.74

aspects.

Figure 5: Pollutant normalization assignment. Each point represents one station–pollutant pair. Colors distinguish variables, while marker shapes indicate the assigned normalization operator. Pairs satisfying ρs,p < θρ and νs,p ≥ θν are routed to RevIN, the remaining routed to MinMax. ing the input length from 12h to 24h leads to different performance trends across models. While longer input sequences provide richer historical context, they may also introduce redundancy and noise. Under this setting, AirFlow also shows good performance, with RMSE increasing only marginally from 21.84 to 22.47 (2.88%), whereas AirFormer experiences a larger increase from 22.10 to 24.01 (8.64%). This suggests that AirFlow can effectively retain informative dependencies while suppressing irrelevant historical variations. Figure 6 provides Taylor diagram summarizing the forecasting performance under different input lengths and forecasting horizons on the Beijing PM2.5 dataset. The diagram summarizes multiple complementary evaluation aspects, including correlation, relative variability, and centered root mean square difference. AirFlow appears closer to the observation reference point, indicating better alignment with the ground truth in these evaluation 14

Table 6: Performance comparison of different spatial dependency modeling against AirFlow. Beijing

Model Variant

Tianjin

Hangzhou

RMSE ↓

MAE ↓

R2 ↑

RMSE ↓

MAE ↓

R2 ↑

RMSE ↓

MAE ↓

R2 ↑

25.21 15.29 15.19 14.42

13.97 7.95 8.04 7.47

0.5564 0.8369 0.8390 0.8513

31.27 19.57 19.56 18.87

19.04 11.33 11.47 10.97

0.2316 0.6991 0.6992 0.7124

19.84 12.70 12.89 12.42

12.82 7.50 7.64 7.28

0.3285 0.7247 0.7162 0.7455

Spatial Loss Coord. Embed GCN Fusion AirFlow

Table 7: Performance comparison under different input lengths and forecasting horizons. Best results are in bold.

RMSE ↓ MAE ↓

R ↑

RMSE ↓ MAE ↓

R ↑

RMSE ↓ MAE ↓

16.44 16.48 17.33 15.84 17.02 16.12 15.68 15.98 15.88 16.64 15.93 15.62 15.22 14.42

0.8113 0.8104 0.7903 0.8262 0.7978 0.8186 0.8284 0.8132 0.8239 0.8068 0.8127 0.8297 0.8348 0.8513

18.89 18.34 18.47 16.88 18.27 17.43 17.53 17.97 16.47 19.18 17.30 16.08 16.32 15.73

0.7522 0.7665 0.7630 0.8059 0.7683 0.7891 0.7867 0.7701 0.8118 0.7445 0.8145 0.8192 0.8188 0.8283

23.52 24.28 23.96 22.27 22.71 22.53 22.10 22.23 22.49 24.43 22.63 22.21 22.43 21.84

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Figure 6: Taylor diagram comparing the forecasting performance of different models on the Beijing PM2.5 forecasting task under varying input lengths and forecasting horizons. The diagram visualizes the correlation coefficient, relative standard deviation, and centered root mean square difference between model predictions and observations. The Observation point is the ideal forecasting with perfect correlation, matched variability, and zero centered difference. Models located closer to the Observation point indicate better overall agreement with the ground truth.

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Figure 7: Comparison between ground truth and predicted values for PM2.5 , PM10 , NO2 , and AQI on the 2024 and 2025 test sets from the Beijing dataset.

Table 8: Multi-pollutant Test Set Characteristics Comparison. Dataset

Pollutant

2024 Test Set

2025 Test Set

Mean

Std.

Max

Mean

Std.

Max

Beijing

PM2.5 PM10 NO2 AQI

33.55 60.70 31.46 55.45

37.73 57.07 22.65 45.22

227 562 198 462

25.67 49.74 19.62 50.32

25.93 44.26 18.05 34.06

455 1111 202 500

Tianjin

PM2.5 PM10 NO2 AQI

40.21 69.14 44.44 63.22

35.63 49.33 25.63 41.72

260 188 188 310

32.57 60.70 27.02 59.07

31.90 48.66 21.85 37.84

1048 1186 213 500

Hangzhou

PM2.5 PM10 NO2 AQI

33.39 54.78 38.08 53.52

24.23 32.81 18.22 28.36

175 239 157 225

29.00 48.68 25.40 49.76

23.64 38.77 18.42 31.42

558 843 186 500

Table 9: Case study performance of AirFlow on different time periods. 10/20–12/31 2024

01/01–09/30 2025

Dataset

Pollutant

Beijing

PM2.5 PM10 NO2 AQI

14.42 22.43 12.65 19.24

7.47 13.02 8.55 10.87

0.8513 0.8443 0.6889 0.8184

12.79 24.76 11.02 19.10

7.11 12.87 6.62 10.81

0.7582 0.7532 0.6471 0.7268

Tianjin

PM2.5 PM10 NO2 AQI

18.87 26.87 14.54 22.58

10.97 16.81 9.78 13.48

0.7124 0.7046 0.6793 0.7023

18.13 28.69 12.93 24.16

9.70 16.42 7.98 14.42

0.6746 0.6483 0.6471 0.6657

Hangzhou

PM2.5 PM10 NO2 AQI

12.42 16.88 10.85 14.84

7.28 10.56 7.43 9.02

0.7455 0.7224 0.6453 0.7105

12.23 22.17 9.63 17.15

6.79 10.46 6.06 8.93

0.7306 0.6427 0.7241 0.6767

RMSE ↓ MAE ↓ R2 ↑ RMSE ↓ MAE ↓ R2 ↑

for NO2 further highlights that gaseous pollutants are more sensitive to localized emission sources such as traffic and urban layouts, making them less transferable than particulate matter. These results suggest that AirFlow learns transferable temporal dynamics while retaining sufficient flexibility to adapt to city-specific characteristics, enabling stable performance across both neardomain and far-domain scenarios.

A.4

Visualization of Experimental Results

The figures presented in this section provide an intuitive visual comparison of model performance across different pollutants, evaluation metrics, and datasets. Figures 8 and 9 visualize the comparative RMSE, MAE, and R2 results for each model on three datasets, where the red dashed reference line marks the performance of AirFlow.

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Table 10: Comparative performance of AirFlow and its transfer learning variant AirFlow (TL) on Tianjin and Hangzhou datasets, where models are initialized with pre-trained weights from Beijing and fine-tuned on each target city’s training data. Dataset

Model

Tianjin Hangzhou

PM2.5

PM10 R2 ↑

RMSE ↓

MAE ↓

R2 ↑

RMSE ↓

MAE ↓

R2 ↑

RMSE ↓

MAE ↓

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AirFlow AirFlow (TL)

18.87 18.52

10.97 10.76

0.7124 0.7182

26.87 25.98

16.81 16.37

0.7046 0.7153

14.54 14.32

9.78 9.64

0.6793 0.6832

22.58 22.17

13.48 13.12

0.7023 0.7111

AirFlow AirFlow (TL)

12.42 12.30

7.28 7.17

0.7455 0.7501

16.88 16.64

10.56 10.33

0.7224 0.7319

10.85 10.97

7.43 7.45

0.6453 0.6421

14.84 14.46

9.02 8.77

0.7105 0.7396

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

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