Numerical reservoir simulations are extremely computationally expensive, as they require the repeated solution of large nonlinear algebraic systems derived from the discretized governing equations. With growing demand for real-time optimization, uncertainty quantification, and history matching in digital twin applications, reducing computational cost has become essential. Deep learning (DL)--based surrogate models have emerged as an effective approach for accelerating subsurface flow simulations. Here, we seek to determine which DL architectures are best suited for high-dimensional, transient subsurface flow problems. In this study, we examine the advantages and relative costs associated with training such models, including memory requirements, training speed, accuracy, robustness, and generalization. We conduct a comparative study of several DL architectures commonly used as surrogate models for subsurface flow problems, including U-Net, V-Net, Temporal Convolutional Networks, Fourier Neural Operators (FNO), and a U-Net--enhanced FNO (U-FNO). As a benchmark, we compare the performance of the studied models for geological carbon sequestration to predict transient pressure build-up and CO$_2$ saturation fields. We study the problem of CO$_2$ injection into a single wellbore in a two-dimensional domain, which is parameterized by anisotropic, heterogeneous permeability and porosity fields, injection configurations, and reservoir properties. Results demonstrate that surrogate model performance is strongly dependent on the underlying PDE type (i.e., hyperbolic vs. elliptic). The U-FNO achieves the highest accuracy for predicting CO$_2$ saturation fields, while the FNO provides the best performance for pressure build-up prediction.

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