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With the increment of interest in leveraging machine learning technology in safety-critical systems, the robustness of neural networks under external disturbance receives more and more concerns. Global robustness is a robustness property defined on the entire input domain. And a certified globally robust network can ensure its robustness on any possible network input. However, the state-of-the-art global robustness certification algorithm can only certify networks with at most several thousand neurons. In this paper, we propose the GPU-supported global robustness certification framework GROCET, which is more efficient than the previous optimization-based certification approach. Moreover, GROCET provides differentiable global robustness, which is leveraged in the training of globally robust neural networks.