Interpretable PM2.5 Forecasting for Urban Air Quality: A Comparative Study of Adaptive Time-Series Models

Moazzam Umer Gondal; Hamad ul Qudous; Asma Ahmad Farhan; Sultan Alamri

cs.LGMar 26, 2026

Interpretable PM2.5 Forecasting for Urban Air Quality: A Comparative Study of Adaptive Time-Series Models

Authors: Moazzam Umer Gondal, Hamad ul Qudous, Asma Ahmad Farhan, Sultan Alamri

Organizations: School of Computing, National University of Computer & Emerging Sciences (FAST), Lahore 54000, Pakistan · College of Computing and Informatics, Saudi Electronic University, Riyadh, 11673, Saudi Arabia

Abstract

Accurate short-term air-quality forecasting is essential for public health protection and urban management, yet many recent forecasting frameworks rely on complex, data-intensive, and computationally demanding models. This study investigates whether lightweight and interpretable forecasting approaches can provide competitive performance for hourly PM2.5 prediction in Beijing, China. Using multi-year pollutant and meteorological time-series data, we developed a leakage-aware forecasting workflow that combined chronological data partitioning, preprocessing, feature selection, and exogenous-driver modeling under the Perfect Prognosis setting. Three forecasting families were evaluated: SARIMAX, Facebook Prophet, and NeuralProphet. To assess practical deployment behavior, the models were tested under two adaptive regimes: weekly walk-forward refitting and frozen forecasting with online residual correction. Results showed clear differences in both predictive accuracy and computational efficiency. Under walk-forward refitting, Facebook Prophet achieved the strongest completed performance, with an MAE of $37.61$ and an RMSE of $50.10$ , while also requiring substantially less execution time than NeuralProphet. In the frozen-model regime, online residual correction improved Facebook Prophet and SARIMAX, with corrected SARIMAX yielding the lowest overall error (MAE $32.50$ ; RMSE $46.85$ ). NeuralProphet remained less accurate and less stable across both regimes, and residual correction did not improve its forecasts. Notably, corrected Facebook Prophet reached nearly the same error as its walk-forward counterpart while reducing runtime from $15$ min $21.91$ sec to $46.60$ sec. These findings show that lightweight additive forecasting strategies can remain highly competitive for urban air-quality prediction, offering a practical balance between accuracy, interpretability, ...

Figures & tables

Study	Focus	Relation to this study
( Samal et al., 2019 ; Abuouelezz et al., 2025 )	Statistical, additive, and ML comparisons	Motivates established model families; regions and protocols differ.
( Sankar and Arasu, 2025 )	Wavelet/PCA, optimized features, Bi-LSTM, SHAP	Feature optimization and explanation; our four-gas set is predefined.
( Lakshmi and Krishnamoorthy, 2024 )	Multi-station spatial–temporal attention; 6–48 h	Spatial representation and shorter horizons; our horizon is 168 h.
( Lakshmi and Krishnamoorthy, 2025b )	Winter temporal transfer and multi-head attention	Learned adaptation across seasons; our correction updates a scalar bias.
( Lakshmi and Krishnamoorthy, 2025a )	Centralized cross-pollutant transfer and attention	Multiple targets/stations; our target is one Beijing PM 2.5 series.
( Le et al., 2022 )	Distributed/federated forecasting	Data locality and client heterogeneity are outside our experiment.

Table 1: Selected literature and its relation to the present evaluation.

Figure 1: Forecasting workflow. All fitting and preprocessing use history before each origin. Actual future covariates are supplied under Perfect Prognosis; future targets enter only scoring and subsequent updates.

Partition	$n$	Mean	SD	Median	Q1–Q3	Min–max
Training	35736	217.54	227.30	140.59	58.24–297.84	0.91–1825.93
Test	3787	155.34	216.57	72.02	27.68–163.12	0.00–1407.51

Table 2: Original observed PM 2.5 distributions. Concentrations are in

\mu\mathrm{g}\,\mathrm{m}^{-3}

; SD denotes sample standard deviation and Q1–Q3 the interquartile interval.

Predictor	Pearson $r$	MI	Absolute- $r$ rank	MI rank
NO	0.892	0.739	3	3
NO 2	0.796	0.628	4	4
CO	0.957	1.284	2	2
SO 2	0.726	0.552	5	5
O 3	-0.287	0.270	8	6
NH 3	0.457	0.232	6	7

Table 3: Training-only predictor rankings. MI is estimated on continuous inputs; mRMR uses separately discretized inputs.

Figure 2: Pearson correlations on 35,732 complete initial-training rows after invalid-input masking. Associations do not establish causal effects.

Figure 3: Training-only continuous mutual information between each candidate predictor and the original target. These descriptive scores do not select the primary subset of four gases.

Family	Configuration	Validation MAE
SARIMAX	$(1,0,1)imes(1,0,1,24)$ ; no constant; stationarity/invertibility constraints disabled	14.99
Prophet	Additive; daily/weekly/yearly seasonalities; default trend/changepoints; no additional regressor scaling	28.52
NeuralProphet	168 lags/leads; 50 epochs; batch 128; learning rate 0.001; no early stopping; global normalization	27.59

Table 4: Selected training-only configurations, used unchanged in both regimes.

Step	Operation
1	At origin $o_{w}$ , isolate history with timestamps earlier than $o_{w}$ and obtain future covariates under Perfect Prognosis.
2	Refit parameters/scaler from history (Regime 1), or retain them and refresh state/context (Regime 2).
3	Produce 168 aligned base predictions; apply $b_{w}$ for frozen correction before current outcomes are revealed.
4	After the week, score only shared observed target/covariate hours; retain partial-week coverage counts.
5	Use base residuals from scored hours to update $b_{w+1}$ ; make revealed history available at the next origin.

Table 5: Weekly forecasting sequence and information boundaries.

Model	Pooled MAE	Pooled RMSE	Weekly MAE $\pm$ SD	Weekly RMSE $\pm$ SD
SARIMAX	30.43	46.88	30.60 $\pm$ 14.92	41.66 $\pm$ 21.78
Prophet	38.72	51.13	39.01 $\pm$ 11.80	49.15 $\pm$ 14.89
NP (42)	41.95	56.51	42.38 $\pm$ 17.80	52.54 $\pm$ 21.79

Table 6: Weekly walk-forward results on the common observed-hour mask. Weekly and pooled aggregations are distinct.

Figure 4: Chronological weekly MAE comparison of frozen base forecasts and weekly refitting on 23 origins and 3,624 shared scoring hours. NeuralProphet uses seed 42.

Figure 5: Chronological weekly MAE of frozen base forecasts for all 23 origins. NeuralProphet uses seed 42; partial weeks contribute only their observed scoring hours.

Model	Pooled MAE	Pooled RMSE	Weekly MAE $\pm$ SD	Weekly RMSE $\pm$ SD
SAR base	30.48	46.96	30.66 $\pm$ 14.99	41.74 $\pm$ 21.85
SAR + EWMA	29.94	43.80	30.17 $\pm$ 13.13	39.60 $\pm$ 19.07
FBP base	43.93	57.56	44.20 $\pm$ 15.38	54.70 $\pm$ 18.51
FBP + EWMA	37.69	49.97	38.07 $\pm$ 10.84	48.27 $\pm$ 14.08
NP (42) base	53.39	70.17	53.12 $\pm$ 27.68	63.23 $\pm$ 29.65
NP + EWMA	37.62	50.91	38.29 $\pm$ 12.57	48.58 $\pm$ 17.20

Table 7: Frozen base and EWMA-corrected results. Correction uses the previously available bias, with predefined

\alpha=0.3

Figure 6: Weekly MAE distributions for frozen base and EWMA-corrected models over 23 origins. NeuralProphet uses seed 42; the plot summarizes temporal variation rather than uncertainty across training seeds.

Comparison	Difference	95% interval
SAR EWMA – base	-0.49	[-3.91, 2.25]
FBP EWMA – base	-6.13	[-14.01, -0.99]
NP EWMA – base	-9.25	[-18.98, -0.25]
SAR EWMA – FBP EWMA	-7.90	[-11.33, -3.63]
FBP EWMA – FBP refit	-0.94	[-1.90, 0.73]

Table 8: Paired mean weekly MAE differences and descriptive 95% moving-block intervals (2,000 replicates; block length three). Negative values favor the first method; NP losses average three seeds.

Seed	Frozen base	Weekly refit	Frozen + EWMA
42	53.39	41.95	37.62
123	52.37	42.25	38.02
2026	34.89	34.61	35.46

Table 9: NeuralProphet pooled MAE by training seed. These are individual runs, not an ensemble.

Figure 7: MAE by hourly lead for frozen base forecasts, weekly refits, and frozen EWMA correction. NeuralProphet uses seed 42; lead-specific scoring counts reflect observed-hour coverage.

Figure 8: MAE by forecast day over the seven-day horizon, using matched observed hours. NeuralProphet uses seed 42.

Figure 9: Frozen-model correction diagnostics for the predefined

\alpha=0.3

. Residuals are base-model residuals; bias is available before the forecast week and updated only afterwards. NeuralProphet seed-specific behavior is reported in the text and tables.

Method	MAE	RMSE
Last observed value	125.74	198.33
Daily persistence	121.52	202.34
Weekly persistence	152.90	248.65
SAR no inputs	115.24	173.53
FBP no inputs	134.07	190.40
NP no inputs	119.50	177.02

Table 10: Frozen predictor controls and persistence references: pooled errors on the same 3,624 scored hours. NP controls use seed 42; broad-input SARIMAX is unavailable because of nonconvergence.

Input	SARIMAX	Prophet
NO	-36.62	-46.32
NO 2	5.17	35.40
CO	237.06	265.48
SO 2	3.22	-24.94

Table 11: Initial frozen-model regressor coefficients, expressed as a PM 2.5 change in

\mu\mathrm{g}\,\mathrm{m}^{-3}

per one training-input standard deviation, conditional on other inputs and temporal terms.

Family	Fits	Timer boundary	Median (s)	Range (s)
SARIMAX	22	Optimization only	110.13	51.18–215.06
Prophet	22	Including initialization/import	23.91	16.22–33.74
NeuralProphet	66	Including initialization/import	182.02	170.63–202.59

Table 12: New walk-forward fit times for origins 2–23, excluding preprocessing and prediction. Boundaries differ across implementations and do not support a controlled speed ratio.

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Ammar Kheder, Michael Boy, Zhi-song Liu

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Air-quality forecasting models are commonly evaluated on regional, preprocessed, and normalized datasets, where missing observations are removed or artificially completed. Such protocols simplify comparison but hide the conditions that dominate real monitoring networks: uneven global coverage, structured missingness, heterogeneous pollutant scales, and deployment cost. We introduce AirQualityBench, a global multi-pollutant benchmark designed to evaluate forecasting models under these realistic conditions. The benchmark contains hourly observations from 3,720 monitoring stations over 2021--2025, covers six major pollutants, and preserves provider-native observation masks. Rather than imputing a dense data tensor, AirQualityBench exposes missingness as part of the forecasting problem and reports errors on valid future observations after inverse transformation to physical concentration scales. Evaluating representative spatio-temporal models under this unified protocol shows that strong performance on sanitized datasets does not reliably transfer to global, fragmented monitoring streams. AirQualityBench therefore serves as a realistic testbed for scalable, mask-aware, and physically interpretable air-quality forecasting. All benchmark data, code, evaluation scripts, and baseline implementations are available at GitHub.

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Mar 22, 2026

Benchmarking Scientific Machine Learning Models for Air Quality Data

Accurate air quality index (AQI) forecasting is essential for the protecting public health in rapidly growing urban regions, and the practical model evaluation and selection are often challenged by the lack of rigorous, region-specific benchmarking on standardized datasets. Physics-guided machine learning and deep learning models could be a good and effective solution to resolve such issues with more accurate and efficient AQI forecasting. This research study presents an explainable and comprehensive benchmark that enables a guideline and proposed physics-guided best model by benchmarking classical time-series, machine-learning, and deep-learning approaches for multi-horizon AQI forecasting in North Texas (Dallas County). Using publicly available U.S. Environmental Protection Agency (EPA) daily observations of air quality data from 2022 to 2024, we curate city-level time series for PM2.5 and O3 by aggregating station measurements and constructing lag-wise forecasting datasets for LAG in {1,7,14,30} days. For benchmarking the best model, linear regression (LR), SARIMAX, multilayer perceptrons (MLP), and LSTM networks are evaluated with the proposed physics-guided variants (MLP+Physics and LSTM+Physics) that incorporate the EPA breakpoint-based AQI formulation as a consistency constraint through a weighted loss. Experiments using chronological train-test splits and error metrics MAE, RMSE showed that deep-learning models outperform simpler baselines, while physics guidance improves stability and yields physically consistent pollutant with AQI relationships, with the largest benefits observed for short-horizon prediction and for PM2.5 and O3. Overall, the results provide a practical reference for selecting AQI forecasting models in North Texas and clarify when lightweight physics constraints meaningfully improve predictive performance across pollutants and forecast horizons.

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