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

Prasanjit Dey; Soumyabrata Dev; Angela Meyer; Bianca Schoen-Phelan

cs.LGApr 1, 2026

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

Authors: Prasanjit Dey, Soumyabrata Dev, Angela Meyer, Bianca Schoen-Phelan

Abstract

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.

Figures & tables

Fig. 1: NeuroDDAF framework. Historical pollutant and meteorological sequences are encoded by a GRU and wind-aware GAT, followed by a Fourier-based transport module and latent neural ODE. Physics-guided and residual predictions are fused by an evidential gate with calibrated uncertainty.

Model	Beijing data
Model	1-day		2-day		3-day
	MAE	RMSE	MAE	RMSE	MAE	RMSE
HA	38.37	45.8	83.91	95.56	50.58	101.51
VAR	60.10	102.92	60.44	103.02	60.64	103.07
DCRNN	35.99	52.55	49.66	67.50	57.01	74.67
STGCN	33.70	49.16	38.93	54.98	43.93	56.57

TABLE I: Performance comparison on the Beijing dataset in terms of MAE and RMSE for 1-day, 2-day, and 3-day forecasts. The best results are highlighted in bold , while the second-best results are underlined .

Dataset	Day	AirPhyNet		NeuroDDAF (Encoder)
				GRU-GAT		GRU		LSTM		TCN		GPT2		Transformer
		MAE	RMSE	MAE	RMSE	MAE	RMSE	MAE	RMSE	MAE	RMSE	MAE	RMSE	MAE	RMSE
Shenzen	1-day	10.55	13.99	11.22	14.85	11.34	15.00	11.30	14.96	10.99	14.59	10.98	14.58	14.26	17.44
	2-day	12.46	16.04	12.73	16.51	12.86	16.72	12.74	16.56	12.30	16.08	12.27	16.05	14.58	17.85
	3-day	13.12	16.50	13.03	16.55	13.12	16.62	13.03	16.60	12.69	16.13	12.72	16.15	15.05	18.05
Tianjin	1-day	29.13	38.34	28.29	36.95	29.39	37.90	28.60	37.37	28.79	37.80	29.76	38.31	29.94	38.64

TABLE II: Performance (MAE and RMSE) for 1-/2-/3-day forecasts across four datasets. AirPhyNet vs. NeuroDDAF encoder variants. The best results are highlighted in bold , while the second-best results are underlined .

Fig. 2: Effect of Physical knowledge in NeuroDDAF, (a) shows MAE in Beijing, (b) shows RMSE in Beijing, (c) shows MAE in Shenzhen, and (d) shows RMSE in Shenzhen.

Fig. 3: Computation-time analysis for NeuroDDAF on Beijing. Epoch time remains stable across training (top-left) and forms a tight distribution (top-right), with consistent spread in the box plot (bottom-left) and near-linear cumulative training time (bottom-right).

Encoder	Params	Batches/epoch	Epoch time (s)	Stop (ep.)
GRU-GAT	75,594	69	$\sim$ 276	24
GRU	71,306	69	$\sim$ 270	25
LSTM	75,594	69	$\sim$ 271	23
TCN	84,362	69	$\sim$ 272	42
Transformer	125,834	69	$\sim$ 273	40
GPT-2	3,440,970	69	$\sim$ 356	22

TABLE III: Empirical runtime and model size on the Beijing dataset (batch size 32, fixed solver tolerances, identical hardware). Avg. epoch time in seconds.

Fig. 4: PM 2.5 spatial distribution in Tianjin on May 1, 2014 at 00:00 (left) and 04:00 (middle) with wind vectors, and their difference (right). Wind-driven transport contributes to localized increases and decreases in concentration.

Appendix figures & tables3 assets

Supplementary material from the paper’s appendix.

Appendix

Quantity	Symbol / Setting
Sequence length	$T=24$ (72 hours at 3-hour resolution)
Forecast horizon	$\tau=24$ (3-day forecast)
Stations / features	$N$ (dataset-specific), $F$ (pollutants+meteo)
Output channels	$d^{\prime}=1$ (PM 2.5 predicted)
Latent dimension	$d_{\ell}=4$
GRU hidden units	$64$ (1 layer)

Appendix

TABLE I: Default hyperparameters and symbols used in experiments and theoretical analysis.

Fig. 1: Geospatial representation of PM 2.5 in Tianjin at 00:00 (left) and 04:00 (middle) on May 1, 2014, and their difference (right). Station identifiers, wind vectors, and an OpenStreetMap basemap provide geographic context to the transport patterns.

Fig. 2: PM 2.5 regime classification. (a) Counts of diffusion-, advection-, and other regimes, where “other” corresponds to time steps with intermediate wind speeds or weak gradients that do not meet thresholds for either transport regime. (b) Example of a diffusion-dominated case with smoother gradients. (c) Example of an advection-dominated case with directional variability under strong winds.

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