Hybrid Sparrow Search Algorithm Support Vector Machine Regression Bidirectional Long-Short Term Memory (SSA-SVR-BiLSTM) model with Lagrange-based weighting for PM$$_{2.5}$$ prediction and stratified evaluation

Abstract Air pollution is a major environmental risk to public health, strongly associated with cardiovascular and respiratory diseases. According to the World Health Organization, at least 99% of the global population lives in areas that do not meet its air-quality guidelines. PM $$_{2.5}$$ 2.5 variability reflects the interaction between local emission sources and meteorological processes that regulate near-surface dispersion and accumulation, producing nonlinear temporal patterns that motivate hybrid modeling approaches. We propose an SSA-SVR-BiLSTM framework for short-term PM $$_{2.5}$$ 2.5 forecasting that combines SSA-optimized SVR and BiLSTM models within a constrained linear ensemble with weights estimated exclusively on the validation partition using Lagrange multipliers. The model is evaluated on 10 months of high-frequency (5-min) air-quality and meteorological data collected at a traffic-influenced monitoring site in Duitama, Colombia. On the held-out test set, the hybrid achieved $$R^2 = 0.9585$$ R 2 = 0.9585 and MAPE $$= 7.62\%$$ = 7.62 % , outperforming five of six SSA-optimized baselines; the difference relative to the best individual model (SSA-SVR was statistically significant but practically negligible ( $$p = 0.0105$$ p = 0.0105 , $$\Delta R^2 = 0.0002$$ Δ R 2 = 0.0002 ), and the value of the hybrid lies primarily in its improved consistency across low and medium concentration regimes rather than in a large global accuracy gain. Stratified evaluation across concentration regimes and normative thresholds (WHO, EPA) revealed systematic underestimation at extreme pollution episodes, a structural limitation shared by all evaluated models. A feature occlusion analysis identified PM $$_5$$ 5 and PM $$_{10}$$ 10 as the dominant exogenous predictors (53.6 and 21.7%), with meteorological variables contributing an additional $${\sim }20\%$$ ∼ 20 % of the total relevance.