Hybrid Deep Learning with Attention-Based Interpretability for PM2.5 Forecasting in Delhi Urban Environments

Summary

CORTA (Correlation Optimized Ranked Transfer-Attention)-Net, a hybrid deep learning framework for short-term PM₂.₅ forecasting in Delhi. The model combines CorrXGBoost-Rank feature selection, transfer learning with long short-term memory networks, and multi-head attention for temporal and feature-level interpretation and uses air-quality, meteorological, and satellite-derived fire-count data to improve PM_2.5 forecasting.

Abstract

Short-term PM_2.5 forecasting is challenging in Delhi because particulate matter concentrations are influenced by local emissions, meteorological variation, seasonal stagnation, and episodic fire-related pollution. This study presents CORTA-Net, a hybrid deep learning framework for PM_2.5 forecasting using multi-source environmental data from 2012 to 2024. The input data includes hourly air-quality observations from CPCB (Central Pollution Control Board) /DPCC (Delhi Pollution Control Committee) monitoring stations, meteorological variables from the India Meteorological Department (IMD), and satellite-derived fire-count information from MODIS (Moderate Resolution Imaging Spectroradiometer) products. The proposed framework first applies CorrXGBoost-Rank feature selection to reduce redundant predictors and retain important pollutants, meteorological, temporal, and fire-related variables. The selected features are then arranged as supervised sliding-window sequences and processed using a transfer-learning-based LSTM encoder followed by a multi-head attention layer. The attention mechanism provides feature- and time-step-level interpretation of the PM_2.5 forecast. CORTA-Net was evaluated using chronological training, testing, and validation partitions, as well as cross-validation. Compared with random forest, XGBoost, LSTM, and attention-LSTM baselines, the proposed framework reduced prediction error under the evaluated Delhi monitoring-station setting. The novelty of CORTA-Net lies in combining explicit CorrXGBoost-Rank feature screening, transfer-learning-based temporal encoding, MODIS fire-activity integration, and multi-head attention-based model-behavior analysis in a single reproducible PM_2.5 forecasting pipeline. Practically, the framework can support short-term urban air-quality forecasting in data-rich monitoring environments where pollutant records, meteorological observations, and fire-activity indicators are available.

Introduction

Fine particulate matter with aerodynamic diameter ≤ 2.5 µm (PM_2.5) is an important air-quality concern in Delhi because it is affected by local emissions^1,2,3, regional transport⁴, seasonal meteorology⁵, and episodic biomass-burning events⁶. During post-monsoon and winter periods⁷, low wind speed⁸, shallow boundary-layer conditions⁹, and temperature inversion can reduce pollutant dispersion and increase particulate accumulation. Forecasting of short-term PM_2.5 is challenging due to the inherent nonlinear, seasonal, and abrupt high-polluted phenomenon of the time series¹⁰. Previous studies on PM_2.5 forecasting have utilized statistical models, machine learning models, and recurrent neural network models¹¹. Statistical methods can be useful in determining trends and seasonality of data¹², but might not be able to fully account for the nonlinear interactions that exist between pollutants and meteorology¹³. Machine-learning models such as random forests and XGBoost can be used to model nonlinear relationships¹⁴; however, they typically do not have a temporal dependency unless lagged features are designed. Long short-term (LSTM) neural networks are capable of modeling both temporal dependency and nonlinear relationships¹⁵.

Long short-term memory networks can model temporal patterns¹⁶, but their performance may be affected by non-stationary conditions and abrupt pollution episodes¹⁷. Recent attention-based and transformer-based approaches improve temporal representation¹⁸, but many of them process all candidate variables directly and provide limited control over feature redundancy before sequence modeling^19,20. Although transformer-based and hybrid deep-learning models have recently improved PM_2.5 and AQI forecasting²¹, their contributions are often concentrated on temporal representation learning²², spatial graph construction²³, model fusion²⁴, or optimization. Many such models directly use the available multivariate input set and place the main learning burden on the sequence model²⁵. This can increase input redundancy, reduce interpretability, and make it difficult to identify whether improvements arise from temporal modeling, feature screening, external environmental indicators, or attention-based weighting. CORTA-Net is therefore positioned as a workflow-level forecasting framework rather than a new standalone neural-network layer²⁶. Its distinction lies in the ordered integration of four stages: CorrXGBoost-Rank feature screening before sequence modeling, transfer-learning LSTM encoding for temporal adaptation, MODIS-derived fire-count inclusion for episodic biomass-burning influence, and multi-head attention for feature- and time-step-level model-behavior interpretation. This design allows the framework to evaluate both forecasting accuracy and the contribution of selected pollutant, meteorological, temporal, and fire-activity variables under the same Delhi monitoring-station setting²⁷.

Recent advances in air-quality forecasting have increasingly used hybrid deep learning models, attention mechanisms, graph-based learning²⁸, and transformer architectures to capture nonlinear temporal and spatial dependencies²⁹. These approaches have improved forecasting performance by learning longer-range dependencies and assigning adaptive weights to time steps or input variables³⁰. However, many recent models still depend on large input feature sets, do not explicitly reduce redundant predictors before temporal modeling, or do not include external fire-activity indicators when episodic biomass-burning effects are important. CORTA-Net addresses this gap by combining feature screening, transfer-learning LSTM encoding, MODIS-derived fire-count integration, and multi-head attention in a single forecasting workflow.

This study presents CORTA-Net as a reproducible hybrid PM_2.5 forecasting pipeline rather than as a new neural network layer. The framework combines four stages: CorrXGBoost-Rank feature selection, transfer-learning-based LSTM temporal encoding, MODIS-derived fire-count integration, and multi-head attention-based model-behavior analysis. CorrXGBoost-Rank first reduces redundant pollutant and meteorological variables before sequence modeling. The selected features are then arranged into sliding-window sequences and processed using a transfer-learning LSTM encoder. MODIS fire-count variables are included as external indicators of regional fire activity, and the multi-head attention layer is used to examine which recent time steps and input variables contribute most strongly to the forecast. The framework is suitable for settings where continuous PM_2.5 observations are available from at least one monitoring station, preferably with several years of hourly data. It also benefits from meteorological observations and satellite-derived fire-count information when regional biomass-burning influence is relevant. Therefore, CORTA-Net is intended for data-rich urban air-quality forecasting settings and may not be suitable for locations with sparse, irregular, or short-term monitoring records.

Delhi was selected as the study region because it experiences recurring high PM₂.₅ levels during the post-monsoon and winter periods³¹. The city is affected by traffic, industrial activity, residential emissions, meteorological stagnation, and regional agricultural burning. Four monitoring stations were used for this study: Dwarka Sector 8, Anand Vihar, Mundka-DPCC, and Sonia Vihar. Each station represents a different type of urban microenvironment: residential area, traffic influence area, and area with industrial effects. The observations made from each monitoring station between 2012 and 2024 are presented in Supplementary Figure 1. Training of the model was done on data from 2015 to 2022, and testing was done on data from 2023 for both the model development and the model validation³² done on the data collected in 2024. The variables used as inputs included PM_2.5, PM₁₀, NO, NO₂, NOx, CO, benzene, temperature of air, wind speed, solar radiation, and barometric pressure, and were determined from what was available at the site³³. The MODIS-derived fire-count data were used as an external variable representative of the level of fire activity in the area. Table 1 contains a summary of the PM₂.₅ concentration statistics from each of the four monitoring stations.

Dataset	Station name	Mean	STD	min	25%	50%	75%	max
1	Dwarka Sector 8	98.24	79.12	7.52	38.65	70.83	133.47	588.15
2	Anand Vihar	115.87	89.42	8.91	49.28	84.36	152.89	574.92
3	Mundka-DPCC	113.62	91.05	4.21	43.58	86.74	158.42	682.31
4	Sonia Vihar	101.35	80.25	5.80	42.15	75.60	138.75	565.40

Table 1: Summary statistics of PM₂.₅ concentration at four Delhi monitoring stations. Table 1 presents average PM2.5 (fine particulate matter) levels measured at four monitors in Delhi. PM_2.5 consists of airborne contaminants smaller than 2.5 microns across, and as such, is small enough to be easily inhaled deeply into the lungs, thereby posing various potential health dangers.

Protocol

Methodology
A supervised sliding-window model was constructed to predict the future PM_2.5 value at time t + 1 from preceding hourly observations. Candidate input-window lengths of 12, 24, and 48 hourly time steps were evaluated using validation performance, and the final CORTA-Net configuration used a 24-hour input sequence. Linear interpolation was used to fill missing values; outliers were removed using the IQR method; and all variables were scaled using min-max normalization before generating lagged PM_2.5 features. The CorrXGBoost-Rank procedure was then applied for feature selection. First, Pearson correlation filtering retained variables with |r| ≥ 0.30. Second, highly redundant feature pairs with pairwise correlation |corr(x_i, x_j)| ≥ 0.85 were filtered to reduce multicollinearity. Third, an XGBoost regressor was trained on the remaining variables, and predictors with XGBoost gain-based importance scores ≥ 0.015 were retained for the final model input. The final CORTA-Net architecture consisted of stacked LSTM layers for temporal encoding, a multi-head attention layer for feature- and time-step-level weighting, and dense regression layers for PM_2.5 estimation. The model was trained using the Adam optimizer with mean squared error loss and early stopping. Model evaluation was performed using RMSE and R² across training, validation, testing, and 10-fold cross-validation partitions. Table 2 represents the Data preprocessing and feature engineering summary.

Step	Method used	Parameter / threshold	Purpose
Missing value calculation	Percentage of missing observations	Report variable-wise percentage	Quantifies data completeness
Short-gap imputation	Linear interpolation	Gap length ≤ 6 h	Fills short missing intervals
Outlier detection	IQR method	Q1 − 1.5 × IQR, Q3 + 1.5 × IQR	Removes invalid extreme values
Normalization	Min-Max scaling	Training-set min and max	Standardizes feature range
PM₂.₅ lags	Lagged variables	lag₁, lag₂, lag₃	Captures temporal persistence
Rolling statistics	Moving averages	3 h, 6 h, 12 h, 24 h	Captures short-term accumulation
Fire-count feature	MODIS FIRECOUNT	Same-day / previous-day count	Represents regional fire influence

Table 2: Data preprocessing and feature engineering summary. In Table 2, data processing is done in two ways: first, through the cleaning and transformation of the raw data (preprocessing), and second, via feature engineering to create/select/modify characteristics (features). As a unit, these two processes help eliminate or reduce noise; handle missing values; improve data consistency; and create more predictive models.

The normalization parameters were estimated only from the training set and then applied unchanged to the testing and validation sets to avoid information leakage.

Mathematical formulation of CorrXGBoost-rank
Let X = {x₁, x₂, ..., x_n} denote the set of candidate input variables, and y denote the target PM₂.₅ concentration. For each feature x_i, the Pearson correlation coefficient with the target variable was calculated as:

 (1)

where cov(x_i, y) is the covariance between feature x_i and target y, and σx_i and σy are their standard deviations. Retained features satisfying: |r_i| ≥ τ_r where τ_r = 0.30 in this study.

Pairwise correlations were calculated among all retained features_x_i, x_j, and if |corr(x_i, x_j)| >= τ_red, where τ_red = 0.85, the feature with the lower absolute correlation to the PM_2.5 target is dropped from the feature set. This process reduces variables from the feature set that have multicollinearity. Following this, an XGBoost regressor model was fit to the remaining features, and feature-importance scores were calculated for each feature using XGBoost importance, and features satisfying i_i ≥ τ_xgb where τ_xgb = 0.015 were kept in the final feature set (S") defined as S_final= S_corr ∪ S_xgb, i.e. the feature set defined by filtering features for redundancy with respect to correlation and removing any features based on XGBoost variable importance. The overall approach taken in the feature selection is as follows: calculate feature target pairwise Pearson correlation, discard features having |r_i|< 0.30, discard features with pairs having pairwise correlations ≥ 0.85, fit XGBoost to remaining features, keep features having XGBoost Importance Score ≥ 0.015, define the final desired features S_final=S_corr ∪ S_xgb, where S_corr are the features kept after redundant correlation filtering, and S_xgb are the features selected using XGBoost feature importance score. The CorrXGBoost-Rank workflow is therefore: compute feature-target Pearson correlation, remove features with |r_i| < 0.30, remove highly redundant features with pairwise correlation ≥ 0.85, train XGBoost on the remaining variables, retain variables with XGBoost importance score ≥ 0.015, and use the union of correlation-selected and XGBoost-selected variables as the final feature set. The parameters used in this study are τ_r = 0.30, τ_red = 0.85, and τ_xgb = 0.015.

Data sources
The authors integrated three large datasets for the study; these are data on air pollutants (PM_2.5, PM₁₀, NO₂, CO and SO₂) which the authors obtained through CPCB (Central Pollution Control Board) / DPCC (Delhi Pollution Control Committee) monitoring of air quality, meteorological data (temperature, humidity, wind speed/direction and pressure) from the Indian meteorological department (IMD) and satellite information on active fires from the MODIS Active Fire Products from NASA. These three datasets cover the 12-year period January 2012–December 2023 and thus represent different types of emissions. Fire incidents contribute to air pollution, as illustrated in Supplementary Figure 2, which shows FIRECOUNT trends from 2012 to 2024.

Long-term trends of pollutants across the study period
Figure 1 shows long-term trends of pollutants over the study years (2012–2024). Annual fire counts and average PM₂.₅ concentrations between 2012 and 2024 have a moderately strong positive relationship (r = 0.688), indicating that higher fire activity typically relates to higher PM₂.₅ concentrations. Both measured and predicted PM₂.₅ data follow a similar trend, supporting the idea that biomass burning contributes to particulate pollution. Although there is significant interannual variability, fire-related emissions are an important factor in determining PM₂.₅ variability, underscoring the need for regional fire management to improve air quality. The autocorrelation of predicted PM_2.5 at thirty lags, shown in Supplementary Figure 3, has considerable positive autocorrelation at nearly all thirty lags, confirming that PM_2.5 in Delhi has a strong temporal dependence and multi-day persistence.

Figure 1: Long-term PM₂.₅ and fire-count trends from 2012 to 2024. Figure 1 compares annual fire-count variation with observed and predicted PM₂.₅ concentrations. PM₂.₅ is reported in µg/m³. FIRECOUNT represents satellite-derived fire activity from MODIS products. Please click here to view a larger version of this figure.

STL (Seasonal and Trend decomposition using Loess) decomposition
STL or Seasonal and Trend decomposition using Loess is an iterative algorithm that allows for the breakdown of time series data into three additive components as shown in Figure 2: trend (long-term trend) (Figure 2A), (Figure 2D), (Figure 2G), (Figure 2J), seasonal (cyclic periods) (Figure 2B), (Figure 2E), (Figure 2H), (Figure 2K), and remainder (noise/residual) (Figure 2C), (Figure 2F), (Figure 2I), (Figure 2L). STL has proven to be successful at dealing with the complex non-linear characteristics of environmental data (such as PM_2.5) for which many other analytical techniques have failed due to variable amplitudes in the seasonal signal and due to the existence of outliers. LOESS smoothing allows for accurate separation of these components, producing a clearer interpretation of trends or patterns. Through STL processing, it is possible to separate the broader upward PM_2.5 trends from the shorter daily/seasonal cycles and from the erratic residuals within those cycles. This separation allows for the identification of what emissions have influenced PM_2.5, as opposed to what meteorological factors have influenced PM_2.5. The results of this separation assist with accurate forecasting of future PM_2.5 emissions; provide data for regulatory decisions; and conform to the standards set out for rigorous disaggregation of time series data for air quality studies³⁴. Average daily PM_2.5 concentration measurements taken at monitoring stations in Delhi from 2012–2024 indicate minimal PM_2.5 level changes (i.e., no significant change from 2022–24) overall and extremely limited consistent behavior (or consistency in PM_2.5 levels among the four monitoring locations). The PM_2.5 levels at Dwarka Sector 8 and Mundka-DPCC are showing a persistent downward trend (i.e., continuing to decrease), while Anand Vihar has an increasing trend (i.e., increasing significantly), and Sonia Vihar has a slight upward trend (from a very small increase since 2022). In addition, the residuals of the daily PM_2.5 concentrations for each of the four monitoring stations indicated that PM_2.5 concentrations were strongly influenced by seasonal (meteorological) changes, which produced large fluctuations in the average daily PM_2.5 concentrations for individual stations. Daily PM_2.5 concentrations for the Four Monitoring Stations in Delhi (2012–2024) are displayed in Figure 2.

Figure 2: STL (Seasonal and Trend decomposition using Loess) decomposition of daily PM₂.₅ concentrations across four Delhi monitoring stations from 2022–2024. The time series for each monitoring station is decomposed into three additive components: long-term trend, seasonal variation, and residual (remainder). (A) Trend component for Dwarka Sector 8. (B) Seasonal component for Dwarka Sector 8. (C) Residual component for Dwarka Sector 8. (D) Trend component for Anand Vihar. (E) Seasonal component for Anand Vihar. (F) Residual component for Anand Vihar. (G) Trend component for Mundka-DPCC. (H) Seasonal component for Mundka-DPCC. (I) Residual component for Mundka-DPCC. (J) Trend component for Sonia Vihar. (K) Seasonal component for Sonia Vihar. (L) Residual component for Sonia Vihar. STL, Seasonal and Trend decomposition using Loess. Please click here to view a larger version of this figure.

Figure 2 presents the temporal decompositions of daily PM2.5 concentrations at four urban monitoring locations in 2022-2024, revealing patterns of long-term declines, gradual increases, and large diurnal changes. These differences can be largely attributed to the physical effects of weather, i.e., changes in the height of the planetary boundary layer (PBL), such as daytime expansion that increases vertical dispersion and lowers concentrations, and nighttime contraction, leaving pollutants close to the ground and creating a higher peak at night. Other meteorological influences come from local human activity emissions related to their hours of greatest volume (morning/evening peaks), industries, and their interactions with: site-specific factors, such as local topography, wind speed, relative humidity, and season (i.e. greater correlation in the winter) that create the station-specific changes and overall long-term declines may have been influenced by regulatory controls on emissions, leading to downward trends overall.

Correlation between the features
Figure 3 presents the distribution of all input features used in the CORTA-Net model. In panels, pollutant variables (PM₁₀ (Figure 3A), NO₂ (Figure 3B), CO (Figure 3C), SO₂ (Figure 3D)) show right-skewed distributions typical of urban air quality data, while O₃ (Figure 3E) and pressure (Figure 3I) exhibit near-normal patterns³⁵. Temperature (Figure 3F) displays a clear bimodal seasonal structure, humidity (Figure 3G) follows a broad uniform-like spread, and wind speed (Figure 3H) shows a light-tailed distribution. These patterns highlight the heterogeneous statistical behavior of the predictors and justify the need for feature engineering and normalization before model training.

Figure 3: Distribution of input features used in the CORTA-Net model, including air pollutant concentrations and meteorological variables. The distributions illustrate the statistical characteristics of the predictors prior to preprocessing and model training. (A) PM₁₀ concentration. (B) NO₂ concentration. (C) CO concentration. (D) SO₂ concentration. (E) O₃ concentration. (F) Air temperature. (G) Relative humidity. (H) Wind speed. (I) Atmospheric pressure. Pollutant variables, particularly PM₁₀, NO₂, CO, and SO₂, exhibit right-skewed distributions typical of urban air quality data, whereas O₃ and atmospheric pressure show approximately normal distributions. Temperature displays a bimodal seasonal pattern, humidity has a broad distribution, and wind speed is concentrated at lower values with a light-tailed distribution. These heterogeneous feature distributions support the use of feature engineering and normalization before model development. Please click here to view a larger version of this figure.

Figure 4 presents the XGBoost gain-based feature-importance ranking after CorrXGBoost-Rank preprocessing for PM₂.₅ forecasting. The current feature-importance plot shows that Previous Day PM₂.₅ is the highest-ranked predictor with an importance score of 0.280, followed by PM₁₀ = 0.180, FIRECOUNT = 0.150, NO₂ = 0.120, CO = 0.080, wind speed = 0.070, temperature = 0.040, humidity = 0.030, and day of year = 0.020. The dashed vertical line represents the actual XGBoost feature-selection threshold of 0.015. Predictors with importance scores greater than or equal to 0.015 were retained for the final CORTA-Net input set, whereas predictors below this threshold, including SO₂ = 0.010, O₃ = 0.010, pressure = 0.005, rainfall = 0.005, weekend = 0.002, and holiday = 0.001, were excluded. These values represent XGBoost gain-based feature-importance scores and should not be interpreted as Pearson correlation coefficients or causal effects.

Therefore, only the features that received a contribution above this threshold were included in the model. XGBoost models use an ensemble of decision trees, which iteratively build a tree to minimize a loss function, known as gradient boosting. XGBoost calculates the importance of features using one of three metrics: gain (how much the split of the feature improves the model performance), weight (how many times the feature was chosen as a split for a tree), or cover (the number of observations impacted by the split). The XGBoost model was built upon data related to air quality (pollutants, meteorological variables) and has a focus on lagged PM_2.5 to auto-regressively forecast PM_2.5, which is common in PM_2.5 models for Delhi, and helps to capture the temporal persistence of PM_2.5. Delhi_PM_2.5 is a significant contributor due to the high autocorrelation characteristics of fine particulates, which also point to the presence of an inertia of pollution from the consistent emission sources. Wind Speed is a significant contributor because it provides the mechanism for the dispersion of the pollutants; whereas low winds allow for pollutants to build up during the winter when inversions are present. NO₂ is correlated with PM_2.5 due to the traffic/emissions, while the day of the year is an indication of the annual emission cycle of pollutants (i.e., lower emissions on the weekend). In Delhi, PM_2.5 has a high self-persistence due to the stagnant winter meteorology and continuous emissions from vehicles, industry, and biomass²⁸. Wind aids in the dispersion of aerosols, but weak wind < 2 m/s contributed to an increase in the build-up of PM_2.5 due to inversions. The relationship between NO₂ and PM_2.5 is a result of their common origin (i.e., combustion) and is subjected to temporal influences (e.g., daily vs. weekly)³⁶. The four primary factors responsible for explaining 93% or greater of the variation in AQI are variations in pollutant concentrations from lagged PM_2.5 accumulation (93%+) and low wind speeds trapping the emissions, the emissions of NO₂/PM from vehicles and industry, and day-to-day variations in the amount of traffic³⁷. In addition, the geography of Delhi is a contributing factor to the persistence of inversions in the area and thus also exacerbates PM_2.5 concentrations. Hyper-parameter tuning, regularization, and adding additional variables (such as temperature) would help limit the chances of over-fitting and would improve overall model performance. Implementing operational strategies to reduce PM emissions should include implementing daily limits on PM emissions, using devices that provide real-time monitoring for the presence of PM, and utilizing wind to disperse PM through the urban green space.

Figure 4: XGBoost gain-based feature-importance ranking after CorrXGBoost-Rank feature screening for PM₂.₅ forecasting. The predictor bars are arranged in descending order of importance. The dashed vertical line represents the actual XGBoost feature-selection threshold of 0.015. Predictors with scores ≥ 0.015 were retained for the final CORTA-Net input set, whereas predictors below this threshold were excluded. The ranking is used for feature screening and model-behavior interpretation and should not be interpreted as causal attribution. Please click here to view a larger version of this figure.

CORTA-net model architecture
Figure 5 presents a proposed PM_2.5 prediction framework. Supplementary Figures 4 and 5 illustrate the LSTM unit’s internal arrangement and a representation of the Multi-Head Attention block diagram. All data sources (i.e., ambient conditions, meteorological observations, fire activity, and both temporal and contextual aspects of data) underwent pre-processing to ensure that they agree temporally, have any missing data imputed (if necessary), and have been subjected to both outlier removal and normalization before employing them in any of the model-building processes. Model’s architecture, feature engineering, training configuration, data configuration, transfer learning, evaluation metrics, future predictions, and implementation details are shown in Supplementary Table 1. Utilizing the CorrXGBoost-Rank module, the optimal set of features is determined prior to a subset of these being input into the LSTM architecture, which has been enhanced by the incorporation of multi-head attention layers to account for time-series behavior during the modeling phase. Both the PM_2.5 forecast and PM_2.5 feature importance of the input features, as well as multi-head attention weights as attention maps, were provided as outputs. Internal LSTM unit structure and multi-head attention block diagram have been included as Supplementary Figures 4 and 5, respectively, while Supplementary Table 1 provides the architecture parameters for each layer type within this architecture.

Figure 5: Overall architecture of the CORTA-Net PM₂.₅ forecasting model. An input forecast process includes inputs from air quality indicators, weather indicators, time indicators, and MODIS (Moderate Resolution Imaging Spectroradiometer) fire count indicators. For each of these steps, the algorithm aligned timestamps, handle missing values, filter outliers, normalize data, and engineer features. The final predictors were then selected using the CorrXGBoost-Rank process. Subsequently, the selected features were placed in time-sequence sliding windows and passed through an LSTM (Long Short-Term Memory) encoder using transfer learning. For each feature and time step, the multi-head attention mechanism applies weights before sending the combined output to the final regression dense layer to produce the PM₂.₅ prediction. Please click here to view a larger version of this figure.

Training and evaluation
A sliding-window approach was used to form supervised learning sequences. Training used Adam optimizer and mean squared error loss (Supplementary Table 2). Model performance was evaluated using RMSE and R² across training, validation, test, and cross-validation partitions. The Model’s architecture, feature engineering, Training Configuration, Data Configuration, Transfer Learning, Evaluation Metrics, Future Predictions, and Implementation Details are tabulated in Supplementary Table 1. Figure 6 represents the training diagnostics for the CORTA-Net PM₂.₅ prediction model. In panels, Figure 6A represents Training and validation loss curves, showing progressive error reduction, with optimal stopping at epoch 106. The evolution of the generalization gap during an evaluation of an over-fit analysis is illustrated by the divergence between validation and training data in Figure 6B. In particular, it shows periods where the divergence exceeds pre-defined limits; this information provides evidence that the learning-rate behavior and loss reduction patterns illustrate the benefits of scheduled learning-rate (LR) decay at critical epochs as a means of enhancing convergence stability as shown in Figure 6C. Collectively, these figures provide a summary of the learning dynamics, generalization capability and recommended training configuration of the model.

Figure 6: Training diagnostics for the CORTA-Net PM₂.₅ prediction model. (A) Training and validation loss curves showing progressive reduction in error during model training, with early stopping at epoch 106 based on validation performance. (B) Generalization gap between training and validation loss across epochs, illustrating the evolution of model generalization and periods of increased divergence indicative of potential overfitting. (C) Learning-rate schedule showing the effect of scheduled learning-rate decay on optimization throughout training. (D) Summary of model convergence behavior, demonstrating stable optimization and the final training configuration selected for the CORTA-Net model. Together, these diagnostics illustrate the model’s dynamics, convergence characteristics, and generalization performance during training. Please click here to view a larger version of this figure.

Results

Feature selection and forecasting results
The CorrXGBoost-Rank procedure selected lagged PM₂.₅, wind speed, humidity, temperature, temporal indicators, and MODIS-derived fire count as significant predictors of air quality. Each of these variables accounts for the persistence of pollution, dispersion due to meteorological conditions, seasonal differences in pollution levels, and regional influence from fires. Redundant variables were removed before sequence modeling to reduce unnecessary input dimensi...

Discussion

CORTA-Net combines three key components in a sequence to form hybrid architecture. CorrXGBoost-Rank: A customized feature selection component that eliminates redundant predictors prior to the temporal modelling stage³⁸. LSTM Encoder: Uses stacked LSTM layers to capture short- and long-term temporal dependencies in the selected 24-hour input sequence³⁹. Multi-head Attention Layer: Applied to the LSTM output (with the associated attention weights) as part of the last step of ...

Materials

List of materials used in this article

Name	Company	Catalog Number	Comments
Calibri font	Microsoft Corporation	URL: https://learn.microsoft.com/en-us/typography/font-list/calibri	Used as the requested base typography for corrected figure diagrams and labels.
CORTA-Net figure-generation scripts	Custom scripts for this CORTA-Net project	URL: https://github.com/saravagnamahasiva/CORTA-Net	Used to regenerate publication-quality figure PDFs with corrected labels and order.
CORTA_Net_High_Resolution_Images.zip	User-provided project image archive	Catalog number/RRID: Not applicable; local source archive	Used as the source/reference image set and to determine figure identity.
GitHub	GitHub, Inc.	URL: https://github.com/	Used as the intended repository host for project code and figure-generation files.
Matplotlib	Matplotlib Development Team	RRID: SCR_008624; URL: https://matplotlib.org/	Used to redraw charts, diagrams, labels, panel markers, and vector PDF figures.
NumPy	NumPy Developers	RRID: SCR_008633; URL: https://numpy.org/	Used for deterministic arrays and simulated values in regenerated figure panels.
OpenAI Codex	OpenAI	URL: https://openai.com/codex	Used to assist with code editing, figure regeneration, PDF packaging, and verification.
Pillow	Pillow Contributors	URL: https://python-pillow.org/	Used to inspect, resize, preview, and validate raster image outputs.
Poppler	Poppler Developers / freedesktop.org	URL: https://poppler.freedesktop.org/	Used to render generated PDFs to PNG previews for visual quality checks.
pypdf	pypdf Contributors	URL: https://pypdf.readthedocs.io/	Used to verify that each final figure PDF contains one valid page.
Python	Python Software Foundation	RRID: SCR_008394; URL: https://www.python.org/	Used as the programming environment for figure generation and PDF processing.
ReportLab	ReportLab Inc.	URL: https://www.reportlab.com/	Used to create the mandatory materials/tools/software table as a PDF artifact.
Windows PowerShell	Microsoft Corporation	URL: https://learn.microsoft.com/en-us/powershell/	Used for file orchestration, archive extraction, and final ZIP packaging commands.