SFDformer: a frequency-based sparse decomposition transformer for air pollution time series prediction

Introduction With the rapid advancement of industrialization and the prevalent occurrence of haze weather, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m1"><mml:mrow><mml:mi>P</mml:mi><mml:msub><mml:mrow><mml:mi>M</mml:mi></mml:mrow><mml:mrow><mml:mn>2.5</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math> contamination has emerged asa significant threat to public health and environmental sustainability. The concentration of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m2"><mml:mrow><mml:mi>P</mml:mi><mml:msub><mml:mrow><mml:mi>M</mml:mi></mml:mrow><mml:mrow><mml:mn>2.5</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math> exhibits intricate dynamic attributes and is profoundly correlated with meteorological conditions as well as the concentrations of other pollutants, thereby substantially augmenting the complexity of predictive endeavors. Methods A novel predictive methodology has been developed. It integrates time seriesfrequency domain analysis with the decomposition of deep learning models. This approach facilitates the capture of interdependencies among high - dimensional features through time series decomposition, employs Fourier Transform to mitigate noise interference, and incorporates sparse attention mechanisms to selectively filter critical frequency components, thereby enhancing time - dependent modeling. Importantly, this technique effectively reduces computational complexity from <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m3"><mml:mrow><mml:mi>O</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:math> to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m4"><mml:mrow><mml:mi>O</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>L</mml:mi><mml:mo>⁡</mml:mo><mml:mi>log</mml:mi><mml:mo>⁡</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:math> . Results Empirical findings substantiate that this methodology yields notably superior predictive accuracy relative to conventional models across a diverse array of real-world datasets. Discussion This advancement not only offers an efficacious resolution for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m5"><mml:mrow><mml:mi>P</mml:mi><mml:msub><mml:mrow><mml:mi>M</mml:mi></mml:mrow><mml:mrow><mml:mn>2.5</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math> prediction tasks but also paves the way for innovative research and application prospects in the realm of complex time series modeling.