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Modern distribution systems are confronted by increasing penetration of distributed energy resources, making state estimation a critical application for distribution systems. However, existing state estimation schemes are often time-consuming and therefore, hard to scale up for large systems. In this context, this paper has proposed using a surrogate model to accelerate state estimations. Long-short-term memory (LSTM) recurrent neural networks have been applied to produce a fast yet coarse surrogate of the system states, which captures the temporal correlations between consecutive states. We have further applied an autoencoder to reduce the input size of LSTM networks, thereby shrinking LSTM network size and increasing the scalability of the proposed method. The surrogate states from LSTM are then fed into the forward/backward sweep state estimator as initial values. As a result, the state estimation convergence is accelerated by the LSTM surrogates. The proposed method is tested on IEEE 123-bus and 8500-node three-phase unbalanced test systems. Experimental results show that the proposed LSTM networks significantly reduce the computational time of distribution systems state estimation.