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Fast and accurate modeling of MR signal responses are typically required for various quantitative MRI applications, such as MR Fingerprinting and MR-STAT. This work uses a new EPG-Bloch model for accurate simulation of transient-state gradient-spoiled MR sequences, and proposes a Recurrent Neural Network (RNN) as a fast surrogate of the EPG-Bloch model for computing large-scale MR signals and derivatives. The computational efficiency of the RNN model is demonstrated by comparing with other existing models, showing one to three orders of acceleration comparing to the latest GPU-accelerated open-source EPG package. By using numerical and in-vivo brain data, two use cases, namely MRF dictionary generation and optimal experimental design, are also provided. Results show that the RNN surrogate model can be efficiently used for computing large-scale dictionaries of transient-states signals and derivatives within tens of seconds, resulting in several orders of magnitude acceleration with respect to state-of-the-art implementations. The practical application of transient-states quantitative techniques can therefore be substantially facilitated.