Thermal error of ball screws seriously affects the machining precision of CNC machine tools especially in high speed and precision machining. Compensation technology is one of the most effective methods to address the thermal issue, and the effect of compensation depends on the accuracy and robustness of the thermal error model. Traditional modeling approaches have major challenges in time-series thermal error prediction. In this paper, a novel thermal error model based on Long Short-Term

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... (LSTM) neural network and Particle Swarm Optimization (PSO) algorithm is proposed. A data-driven model based on LSTM neural network is established according to the time-series collected data. The hyperparameters of LSTM neural network are optimized by PSO and then a PSO-LSTM model is established to precisely predict the thermal error of ball screws. In order to verify the effectiveness and robustness of the proposed model, two thermal characteristic experiments based on step and random speed are conducted on a self-designed test bench. The results show that the PSO-LSTM model has higher accuracy compared with the RBF model and BP model with high robustness. The proposed method can be implemented to predict the thermal error of ball screws, and provide a foundation for thermal error compensation.