## 1 Introduction  
Industrial robots (IRs) are an important part of intelligent manufacturing, which is being increasingly applied to fields with high precision and efficiency requirements, such as robot machining [1, 2], assembly [3], and laser cutting [4, 5]. Dynamic response is one of the most important indicators of IRs in these applications. Accurate dynamic models and response prediction of robots are prerequisites for processing optimization, trajectory planning, and quality prediction [6] before actual operation. Since IRs usually operate in position control mode, the dynamic position prediction of an end-effector (EE) based on the reference input trajectory (Figure 1) plays a vital role in their performance optimization. It is challenging to realize accurate and stable position prediction of IRs due to their high nonlinearity and arbitrarily given motion conditions. Prediction modeling encompasses two primary methodologies: the parametric dynamic model (PDM), which relies on physical principles and insights, and the data-driven model (DDM), leveraging machine learning techniques. A PDM is a comprehensive model that can be divided into a dynamic model of the mechanical system and a servo system model describing the features of electricity and control [7]. The servo system in IRs contains servo motors and their drivers, which are usually configured nested control loops [8]. And the proportional-integral-derivative (PID) algorithm is commonly employed across various control loops [9]. The model of servo systems is well established [10], and the relevant parameters for both controllers and motors are delineated within the documentation provided by the servo drive manufacturers and within the user manuals themselves. An accurate dynamic model of the mechanical system is the key factor for position prediction. The flexible dynamic model [11] can be constructed for describing the mechanical properties, where parameter identification remains an open issue to date. Among the various identification methods frequently employed, the inverse dynamic identification model combined with the least squares (IDIM + LS) technique stands out as a particularly prominent approach [12; 13], where the unknown parameters are grouped into a minimum parameter set and the LS criterion is then employed to estimate parameters based on excitation experiments. On this basis, several literary improvements have been made [14; 15; 16] with different estimation methods such as Kalman filtering [17] and maximum likelihood estimation [18]. In addition, machine learning is also employed in parameter identification. To simplify the identification process, an identification methodology based on convolutional neural network (CNN) was proposed in [19] for a two-degree-of-freedom (DoF) truss robot where the optimization of excitation trajectories is no longer required. The identical CNN-based method was applied to a 2-DoF serial robot in [20]. However, these approaches are oriented to the minimum parameter set and cannot obtain each parameter independently, which limits the flexibility of model application. Moreover, the training dataset for the CNN model in [19; 20] can only be collected from a virtual dynamic model of robot, which restricts the accuracy and reliability of the final model with actual collected input data. The prediction error in the PDM arises inherently from the simplification of the real system during modeling, including linear approximations and the neglect of higher-order terms [21; 22; 23]. [PERSON] et al. [24] built a CNN model to identify the dynamic force acting on a robot EE. Similar CNN models were used for response prediction of multiple mechanical systems in [25]. [PERSON] et al. [26] employed the deep neural network for positioning error modeling of a robot EE, but it is not applicable for the prediction of dynamic response. Figure 1: Dynamic position prediction of EE based on reference trajectory.