# A Categorization of Digital Twin and Model-Based System Engineering Interactions
## 1 Introduction  
In today's rapidly evolving technological landscape, the concept of the digital twin (DT) has emerged as one of the key technologies of Industry 4.0. The DT can be defined as a digital representation of a physical entity or process capable of simulating its behavior and rules. Digital twins can impact different parts of the product life cycle, from design to product maintenance [1]. The popularity of DTs has grown since their creation; however, there is still no agreement or universally accepted concept [2, 3]. [PERSON] is credited with creating the concept of a digital twin in 2003, introducing it as a virtual representation of a physical object. [PERSON] DT was a three-dimensional model that included physical and virtual products, as well as the connection of data between them. However, at that time, technology was not advanced enough to fully support the development of these virtual counterparts, as later noted by the author in 2014 [4]. In 2012, [PERSON] and [PERSON] proposed another influential definition of a digital twin, describing it as an integrated multiphysics, multiscale, probabilistic, ultrafidelity simulation that replicates the behaviors and states of its physical counterpart [5]. Through a literature review, [PERSON] et al. [6] categorized DTs based on the level of integration between physical and digital entities, establishing definitions for termsoften used interchangeably until then. The proposed categories include digital models, digital shadows, and digital twins. In the digital model category, data transfer between physical and digital entities is entirely manual. Consequently, a state change in one does not automatically impact the other. In a digital shadow, there is unidirectional communication from the physical entity to the digital one, meaning that changes in the physical entity are automatically reflected in the digital entity; however, the reverse is not true. Lastly, in a digital twin, there is bidirectional data exchange between entities, allowing direct mutual influence. [PERSON] et al. [7] presented an expanded version of [PERSON] three-dimensional DT model in 2018. Their five-dimensional model, illustrated in Figure 1, includes the physical entity (PE), the virtual entity (VE), the digital twin database (DTD), the service system (SS), and the connections between the parts (CN). The PE represents the actual product or service under monitoring. The VE is a high-fidelity digital model of the physical entity, capable of mirroring its geometry, physical properties, behaviors, and rules. The SS encompasses the services provided by the physical and virtual entities to the stakeholders, shown at top of the image. Digital twins rely heavily on data storage and processing, requiring all exchanged data--such as historical data, metadata, and derived data--to be stored in accessible repositories, represented by the DTD in the image [1]. The connections enable seamless communication between all components of the model, facilitating sensor data transfer from the PE to the VE, the transmission of feedback data from the VE to the PE, and the delivery of commands from the SS to both the VE and PE [7]. [PERSON] et al. [8] suggested a unified definition of a DT by highlighting a series of core properties that allows the digital object to accurately reflect and operate like the physical object within certain defined operational contexts. As a result, a DT system can effectively capture and represent the current state of the physical object, serving as a fundamental realization of the DT concept. The properties are as follows. * Mirroring: all data and information that characterize the physical object are present in the digital counterpart. * Virtualization: the capability to virtualize complete systems using software and run them on general-purpose hardware. * Entanglement: the communication relationship between a physical object and its digital counterpart. * Representativeness: how accurately the digital object reflects the physical object that it represents.