Results from applying SINDy to the TPR (blue lines) and N-body (purple lines) models. The top row shows the SINDy-recovered coefficient P, and the middle row shows coefficient Q, both as a function of R. The bottom row shows the r² value, indicating the goodness-of-fit for the SINDy model at each radius. The black dash-dotted lines represent the analytical predictions for P and Q (Eq. (18)). The coefficients P and Q obtained by fitting the radial derivative (∂V_R/∂t) and the azimuthal derivative (∂V_ϕ/∂t) are shown in the left and right columns, respectively. Voids in the curves correspond to radii where SINDy failed to find a solution.