## 1 Introduction
Considering the sequential characteristics inherent in IRs, where the current state is determined by both the present inputs and the historical inputs and states, it is imperative to apply sequence modeling approaches to capture these dependencies effectively. [PERSON] et al. [27] constructed a multi-gated model to predict kinematics and dynamics using a long short-term memory (LSTM) network, which is one of the prevalent variants of recurrent neural network (RNN) [28]. [PERSON] et al. [29] have developed a predictive learning framework specifically designed for the dynamics forecasting of chaotic robotic systems. This model incorporates a classification of motion states into distinct categories, each warranting separate modeling to enhance the precision of dynamic predictions. However, the efficacy of the classification-based methodology is compromised in the context of IRs; this is mainly attributed to the complex multi-axis interactions and the numerous motion conditions that must be taken into account. Additionally, the end-to-end (ETE) modeling techniques previously discussed are inherently reliant on a substantial dataset for the extraction of salient features, which is a significant limitation in scenarios where data scarcity is prevalent. Meanwhile, since the prediction of DDM relies on the local neighborhood training data, regions with uncharted states and sparse training data pose challenges for effective generalization. To address the respective shortcomings of the PDM and DDM, hybrid modeling approaches are proposed, leveraging the internal knowledge of both. Specifically, DDM is often designed to serve as a compensatory mechanism for the residual errors inherent in the PDM. [PERSON] et al. [30] developed a compensation model utilizing LSTM for forecasting joint torque. And the attention mechanism [31] was also embedded into the neural network. [PERSON] et al. [32] employed an adaptive RNN with a dynamic model for inverse dynamic identification. [PERSON] et al. [33] integrated an adaptive neural network with the rigid-body dynamic model to estimate the response of a robot based on the feedback data from servo drivers. These hybrid models effectively improve the accuracy and stability of prediction. To predict the dynamic tracking error of robot joints, a temporal convolutional network (TCN) is employed in [34] taking into account pose-dependent load decomposition. [PERSON] et al. coupled the data-driven model with the multi-domain analysis model to build the machine tool feed system model [35]. [PERSON] et al. developed a physically guided long short-term memory network for system identification of a servo-hydraulic shaking table [36]. [PERSON] et al. used physics-informed neural networks (PINNs) to model expected ship speeds in still water conditions [37]. [PERSON] et al. propose a physics-informed neural network (PINN) approach to solve the contradiction between accuracy and interpretability in UAV dynamic modeling [38]. However, the training dataset of DDM in this literature selects the reference data as input and the residual error of PDM prediction as output, which is referred to as the ETE dataset in this study. ETE data lack nonlinear dynamic features of robots and thus limits the prediction performance. Since the PDM involves rich physical knowledge of robots, it is reasonable to integrate ETE data and PDM findings to construct the training dataset. In this study, a hybrid-driven dynamic position prediction (HDPP) approach integrating a PDM and machine learning-based DDM is developed. The main contributions are as follows:  
1. A PDM of a robot, including a flexible dynamic model of the mechanical system and a servo system model, is constructed based on theoretical analysis. To obtain independent dynamic parameters, a reinforcement learning (RL)-based parameter identification method is proposed where the CAD model, least squares estimation, and RL are integrated. 2. A DDM based on a novel TCN-LSTM network is established for each joint as the residual error compensator (REC) after PDM prediction.