Abstract The advent of machine learning (ML) has revolutionized the research of plasma confinement, offering new avenues for exploration. It enables the construction of models that effectively streamline the simulation process. While previous first-principles simulations have provided physics-based transport information, they have been inadequate fast for real-time applications or plasma control. In order to address this challenge, we introduce SExFC, a surrogate model based on the Gyro-Landau Extended Fluid Code (ExFC). An approach of physics-based database construction is detailed, as well the validity is illustrated. Through harnessing the power of ML, SExFC offers the capability to deliver rapid and precise predictions, facilitating real-time applications and enhancing plasma control. The proposed model integrates the recurrent neural network (RNN) algorithm, specifically leveraging the Gated Recurrent Unit (GRU) for iterative prediction of flux evolutions based on radial profiles. Therefore, the SExFC model has the potential to enable rapid and physics-based predictions that can be seamlessly integrated into future real-time plasma control systems.