## 1 Introduction
Depending on the possibility of updating the state of the simulation model objects and the direction of data exchange in [16], the authors divided digital mappings into three categories of digital representation of physical objects (a classification of digital twins):  
* Digital Model--which does not use any form of automatic data integration between the physical object and the digital object;
* Digital Shadow--in which there is an automated one-way flow of data between the state of a physical and digital object;
* Digital Twin--where data flows (in both directions) between the existing physical and digital objects are fully integrated. Of course, in the applications of simulation models described above, since the DT is the central element of the CPPS, the DT should have the functionality of the third category. The possibility of bi-directional communication along with the mapping and simulation of the behavior, functioning, and performance of the physical counterpart are only necessary conditions that allow their use as the main element of the cyber layer. For digital twins  
Figure 1: Cyber–physical system and a simulation model as a digital twin. to become useful in supporting decision-making in the areas of planning and control of physical system objects, it is necessary to enrich the cyber layer (or the digital twin itself) with analytical modules that allow for the determination of solutions that can be sent to the control system in real time. The challenges faced by such solutions correspond to the requirements of the third and fourth levels of development of production management and control strategies in the four-level development scale proposed by [PERSON], [PERSON] and [PERSON] [17] concerning manufacturing systems (Figure 2). The first level of development is characterized by the so-called passive (reactive) management and control methods, where most of the data are collected and entered offline, and traditional relational databases can meet most data management requirements. At the next stage, data are collected in real time using RFID tags, sensors, and barcodes, and are transmitted over real-time networks, enabling faster data processing and decision-making. The third and fourth stages ensure the use of appropriately predictive and proactive management and control methods. They will require extensive machine learning applications, artificial intelligence methods, cloud computing, and other big data technologies. The predictive strategy is to be based on combined big data and digital twin technologies. In the case of a proactive strategy, it may even be possible to control physical systems based on the self-adaptation and self-reconfiguration functions of the CPPS. It is an extension of the predictive strategy towards intelligent management and production control, thanks to the combination of artificial intelligence technologies and digital twins. Currently, many companies are still at the first or second stage of development [17]. Similarly, the Digital Twin-based Manufacturing System (DTMS) model proposed in [18] is a novel reference emphasizing fusion, interaction, and iteration. Regarding iteration, the system continuously analyzes the production process and continuously iteratively corrects the DT model to improve the overall DTMS. The authors in [18] point out that the manufacturing industry is currently in an era of rapid and intelligent development thanks to the strengthening of information technologies. In this context, the research on DTMS has become a \"hot topic\" in both academic and industrial circles. The need to respond to changing environmental factors and to autonomously reconfigure the production system or adapt to these changes indicated above in relation to the Industry 4.0 concept highlights the great potential of machine learning applications and the ability to achieve promising results in the field of production research.