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Metasurface has garnered extensive attention across multiple disciplines owing to its profound capability in electromagnetic (EM) manipulations. To determine its EM characteristics accurately, full-wave simulations are essential. These simulations necessitate significant amounts of time and memory resources, hindering the efficiency of the design process. In this article, we propose MetaPhyNet, a novel physics-driven neural network based on temporal coupled-mode theory (CMT) to address the challenges of low efficiency and high memory consumption in large-scale metasurface design. In the proposed approach, a surrogate model is developed to achieve rapid prediction of the EM responses of ultra-large-scale metasurfaces. In comparison with the full-wave EM simulation, the proposed model reduces the simulation time of the ultra-large-scale metasurface by up to two orders of magnitude and the memory consumption by more than two orders of magnitude. Our proposed approach aims to enhance the efficiency and intelligence in metasurface design by leveraging the principles of CMT within a neural network framework. Through this innovative integration of physics-based modeling and machine learning, we seek to achieve significant advancements in the design efficiency of metasurfaces. We apply the proposed model to optimize the design of two metasurface absorbers to showcase the effectiveness of our proposed approach. Simulations and experimental results are provided to demonstrate the value and impact of our approach in addressing existing challenges in full-wave EM simulation-based design optimizations of metasurfaces.