A neural-network based innovative model recognizing the wavenumber space images has been developed to accurately forecast when the saturation of turbulent heat fluxes commences, i.e., the saturation time, in nonlinear gyrokinetic simulations. The wavenumber space images of the perturbed distribution function are focused on, which better represent the characteristics of turbulence. The model exploiting the state-of-the-art convolutional neural network model is capable of detecting minuscule differences between the images. Once the wavenumber space image is fed into the developed model, it can quickly and almost perfectly classify which phase of the turbulence evolution in nonlinear gyrokinetic simulations the image is in: the linearly and nonlinearly growing phases and the saturation phase. It can also predict the simulation time at which the image was processed with significantly high accuracy. The model enables us to forecast the saturation time of the gyrokinetic simulation in question by feeding an image at an early stage of the simulation and receiving the degree of progress toward the saturation. The ability of the model makes it possible to easily search out a desirable initial condition that rapidly conducts the simulation to a saturation phase. Such a pre-prediction model is important for running long time simulations on a large scale supercomputer like Fugaku in view of the efficient use of computational resources. In order to improve the predictive capability for the simulation that is going to be performed, several prediction models are trained by data with different major instabilities. The best predictor is selected to be in use based on the result of the pre-performed linear stability calculation with low computational cost.