Catheters are increasingly being used to tackle problems in the cardiovascular system. However, positioning precision of the catheter tip is negatively affected by hysteresis. To ensure tissue damage due to imprecise positioning is avoided, hysteresis is to be understood and compensated for. This work investigates the feasibility to model hysteresis with a Long Short-Term Memory (LSTM) network. A bench-top setup containing a catheter distal segment was developed for model evaluation.The LSTM was first tested using four groups of test datasets containing diverse patterns. To compare with the LSTM, a Deadband Rate-Dependent Prandtl-Ishlinskii (DRDPI) model and a Support Vector Regression (SVR) model were established. The results demonstrated that the LSTM is capable of predicting the tip bending angle with sub-degree precision. The LSTM outperformed the DRDPI model and the SVR model by 60.1% and 36.0%, respectively, in arbitrarily varying signals. Next, the LSTM was further validated in a 3D reconstruction experiment using Forward-Looking Optical Coherence Tomography (FL-OCT). The results revealed that the LSTM was able to accurately reconstruct the environment with a reconstruction error below 0.25 mm. Overall, the proposed LSTM enabled precise free-space control of a robotic catheter in the presence of severe hysteresis. The LSTM predicted the catheter tip response precisely based on proximal input pressure, minimizing the need to install sensors at the catheter tip for localization.