The turbulent flow induced by a plasma actuator mounted on a flat plate is simulated using the Improved Instability Sensitive Reynolds Stress Model (IISRSM) of Jakirlic and Maduta [1], and novel approaches to model the unsteady plasma actuator (PA) force. The geometry and boundary conditions of the considered flow configuration, which represents a wall-jet developing on a flat plate in quiescent air, are based on the experimental and numerical investigations of Maden et al. [2]. In contrast to the previous relevant work, two different approaches are used here to model the transient PA force. The first approach is based on the measurements of Kuhnhenn et al. [3], using the “exact” measurements of the force at the eight time sequences for an AC discharge cycle of the plasma actuator. The second approach uses the eight measurements as well as additional temporally interpolated force values to train a neural network to output the force value for any spatial and temporal position and is referred to as ML (Machine-Learning) based force. The calculations are performed with the finite volume method-based code OpenFOAM®, where all derived turbulence model equations and appropriate plasma actuator force model formulations are implemented. The results of the simulations, especially with respect to the turbulence intensity enhancement, show a better agreement with the experimental data using the second approach and demonstrate its validity for modeling the transient force of the plasma actuator. Accordingly, further improvements of the results are expected by refining the neural network algorithm.