We introduce a neural network surrogate model that predicts the eigenvalues for the turbulent microinstabilities, based on the gyrokinetic eigenvalue solver in QuaLiKiz. The model quickly provides information about the dominant instability for specific plasma conditions, and in addition, the eigenvalues offer a pathway for extrapolating transport fluxes. The model is trained on a 5×10 6 data points large dataset based on experimental data from discharges at the joint European torus, where each data point represents a QuaLiKiz simulation. The most accurate model was obtained when the task was split into a classification task to decide if the imaginary part of eigenvalues were stable (<= 0) or not, and a regression model to calculate the eigenvalues once the classifier predicted the unstable class.