Mathematical Evaluation of Classical and Quantum Predictive Models Applied to PM2.5 Forecasting in Urban Environments

Jesús Cáceres-Tello () and José Javier Galán-Hernández
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Jesús Cáceres-Tello: Faculty of Mathematics, Complutense University of Madrid, 28040 Madrid, Spain
José Javier Galán-Hernández: Faculty of Statistical Studies, Complutense University of Madrid, 28040 Madrid, Spain

Mathematics, 2025, vol. 13, issue 12, 1-19

Abstract: Air quality modeling has become a strategic area within data science, particularly in urban contexts where pollution exhibits high variability and nonlinear dynamics. This study provides a mathematical and computational comparison between two predictive paradigms: the classical Long Short-Term Memory (LSTM) model, designed for sequential analysis of time series, and the quantum model Quantum Support Vector Machine (QSVM), based on kernel methods applied in Hilbert spaces. Both approaches are applied to real PM2.5 concentration data collected at the Plaza Castilla monitoring station (Madrid) over the period 2017–2024. The LSTM model demonstrates moderate accuracy for smooth seasonal trends but shows limited performance in detecting extreme pollution events. In contrast, the QSVM achieves perfect binary classification through a quantum kernel based on angle encoding, with significantly lower training time and computational cost. Beyond the empirical results, this work highlights the growing potential of Quantum Artificial Intelligence as a hybrid paradigm capable of extending the boundaries of classical models in complex environmental prediction tasks. The implications point toward a promising transition to quantum-enhanced predictive systems aimed at advancing urban sustainability.

Keywords: quantum artificial intelligence; PM2.5 prediction; quantum support vector machine (QSVM); air pollution modeling; long short-term memory (LSTM); quantum kernel; computational efficiency; time series forecasting; environmental data science; urban sustainability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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