A company plans to use supervised machine learning to predict the strength and dissi$-$

pation rate of the wake vortices behind small drones in order to ensure safe operation

in urban environments. Their research team has collected data on several variables that

it thinks might influence the vortex dissipation rate, $lon($units: $\frac{W}{k}g$ or $\frac{m^2}{s^3}),$ in$-$

cluding drone wingspan $b[m],$ Drone velocity $V[\frac{m}{s}],$ Drone mass $m[kg],$ Air density

${}_a[\frac{kg}{m^3}],$ dynamic viscosity of air $[Pa-s],$ and altitude $h[m].$ The magnitude of

gravitational acceleration $g$ also plays a role, though they haven't specifically collected

data on it$.$ The engineers want to avoid overfitting during the ML training and reduce

dimensionality in the dataset before training the machine learning model. Use Bucking$-$

ham Pi theorem to identify the key non$-$dimensional groups they can form from their

data to simplify their training set.