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Abstract Prediction of the spatial‐temporal dynamics of the fluid flow in complex subsurface systems, such as geologic storage, is typically performed using advanced numerical simulation methods that solve the underlying governing physical equations. However, numerical simulation is computationally demanding and can limit the implementation of standard field management workflows, such as model calibration and optimization. Standard deep learning models, such as RUNET, have recently been proposed to alleviate the computational burden of physics‐based simulation models. Despite their powerful learning capabilities and computational appeal, deep learning models have important limitations, including lack of interpretability, extensive data needs, weak extrapolation capacity, and physical inconsistency that can affect their adoption in practical applications. We develop a Fluid Flow‐based Deep Learning (FFDL) architecture for spatial‐temporal prediction of important state variables in subsurface flow systems. The new architecture consists of a physics‐based encoder to construct physically meaningful latent variables, and a residual‐based processor to predict the evolution of the state variables. It uses physical operators that serve as nonlinear activation functions and imposes the general structure of the fluid flow equations to facilitate its training with data pertaining to the specific subsurface flow application of interest. A comprehensive investigation of FFDL, based on a field‐scale geologic storage model, is used to demonstrate the superior performance of FFDL compared to RUNET as a standard deep learning model. The results show that FFDL outperforms RUNET in terms of prediction accuracy, extrapolation power, and training data needs.