Modeling atmospheric data and identifying dynamics Temporal data-driven modeling of air pollutants

Atmospheric modeling has recently experienced a surge with the advent of deep learning. Most these models, however, predict concentrations pollutants following data-driven approach in which physical laws that govern their behaviors and relationships remain hidden. With aid real-world air quality data collected hourly different stations throughout Madrid, we present an empirical using techniques goals: (1) Find parsimonious systems ordinary differential equations via sparse identification nonlinear dynamics (SINDy) model concentration changes over time; (2) assess performance limitations our models stability analysis; (3) reconstruct time series chemical not measured certain delay coordinate embedding results. Our results show Akaike’s Information Criterion can work well conjunction best subset regression as to find equilibrium between sparsity goodness fit. We also that, due complexity system under study, identifying this longer periods require higher levels filtering smoothing. Stability analysis for reconstructed (ODEs) reveals more than half physically relevant critical points are saddle points, suggesting is unstable even idealized assumption all environmental conditions constant time.