This paper provides details on the optimization of phase and amplitude of perturbations for simulated free shear layer flows. The goal of the optimization is to maximize or minimize the rate of growth of the shear layer, based upon first-principles physics-based simulations that represent solutions to the fully nonlinear Navier-Stokes equations. These simulations have been obtained using a unique method [1, 2] that considerably reduces the computational burden normally associated with obtaining such solutions. In fact, the development of active flow control methodologies is often based upon reduced order models of the Navier-Stokes equations to avoid this computational overhead. Various regression methods were used to approximate the shear layer thickness as a function of the phase and amplitude of perturbations used to excite the flow dynamics as a proxy for using a simulation based upon first principles, in order to reduce computational burden even further. It was found that nonlinear regression methods overall outperformed linear regression methods, owing to the fundamentally nonlinear nature of the data.