## 1 Introduction
In Lahore, winter time PM\({}_{2.5}\) levels have reached daily averages of over 300 ug/m\({}^{3}\), and this is mainly driven by regional crop burning and urban transport [22]. A 2024 study in ten Indian cities found that each 10 ug/m\({}^{3}\) rise in PM\({}_{2.5}\) is linked to a 1-3% increase in daily mortality, accounting for tens of thousands of deaths annually in Delhi and Bengaluru [23]. Meanwhile, time-resolved measurements have shown that PM\({}_{2.5}\) and PM\({}_{10}\) concentrations in Delhi and Beijing are 20-30 times higher than those in urban Europe during peak seasons [24]. However, cities like Beijing have shown that significant improvement is possible. Following the implementation of strict air pollution control measures--such as replacing coal with natural gas, relocating heavy industry, restricting vehicle use, and investing in air quality monitoring infrastructure, the city of Beijing experienced a 50% reduction in annual PM\({}_{2.5}\) concentrations between 2013 and 2020 [25; 26]. These cases highlight not only the need for policy action, but also the importance of preventive tools, such as air quality forecasting models, which enable early warnings and targeted mitigation, thus forming the basis of the present work. Typically, when discussing particulate matter measurements that directly affect the air quality, the most common references are PM\({}_{2.5}\) (fine particulate) and PM\({}_{10}\) (coarse particulate), as defined by the World Health Organization (WHO) [15] and the European Environment Agency (EEA) [16]. However, other particle sizes--those less frequently studied--also play a crucial role in air quality and public health. These include the ultra-fine PM\({}_{1}\) and the intermediate PM\({}_{4}\), which sits between PM\({}_{2.5}\) and PM\({}_{10}\) in terms of size. PM\({}_{1}\) particles, due to their tiny size, can penetrate deep into the respiratory tract and even reach the bloodstream, raising concerns about their implications for cardiovascular and pulmonary health. Studies have highlighted the presence and impact of PM\({}_{1}\) in various environments, such as construction sites, where high concentrations of ultra-fine particles have been reported [27], and urban traffic-exposed locations, which are major sources of fine particulate emissions [28]. Despite its health relevance, PM\({}_{1}\) remains underrepresented in both regulatory frameworks and routine monitoring networks. Similarly, PM\({}_{4}\) is an intermediate-size particulate that receives limited attention despite its potential significance. Unlike the more commonly referenced PM\({}_{2.5}\) and PM\({}_{10}\), PM\({}_{4}\) is less regulated and studied, yet emerging evidence suggests it may act as a transitional indicator of pollution from industrial and mechanical activities. Research has shown that PM\({}_{4}\) concentrations correlate with health indicators and pollutant patterns in industrial and densely populated regions, including its documented physiological effects on respiratory health [29; 30]. Furthermore, studies, such as the one of [PERSON] et al. [31], have emphasized the importance of using a broader spectrum of particulate sizes--including PM\({}_{1}\), PM\({}_{2.5}\), PM\({}_{4}\), and PM\({}_{10}\)--to assess air pollution near construction sites, demonstrating that both fine and coarse particulates contribute to overall pollution loads and human exposure risks. An additional study [32] further supported the inclusion of diverse particulate fractions in air quality models, revealing how they jointly affect both environmental metrics and public health assessments. Given these findings, this study incorporated both PM\({}_{1}\) and PM\({}_{4}\) into its input variables alongside the more standard PM\({}_{2.5}\) and PM\({}_{10}\), aiming to provide a more comprehensive representation of the airborne particulate pollution that is present in localized meteorological conditions and forecasted Air Quality Index (AQI) levels. Accurate air quality predictions are a necessity these days.