## 3 State of the Art in Digital Twins and Cyber-Ranges
### State of the Art in Digital Twins
One of the main objectives of the approach is to reduce the needed and expensive expert knowledge for the DT construction. [PERSON] et al. [64] introduced a reference architecture for a version of DTs called \"digital twin-based cyber-physical production system.\" This architecture relies on external construction of the virtual replica of the system and focuses on adding components and data flows for enabling automated control. [PERSON] and [PERSON] [65] explored the potentials of available open source tools and services, which can help developing an open source DT ex nihilo. They proposed a DT concept based on a micro-services architecture to design a flexible, open source solution for digital twins and make it accessible to a wider industrial and research audience. This remains however more of a conceptual proposal than an actual open-source tool for DT development. Another reference architecture based on micro-services was introduced by the consortium of the research project MAYA [58]. The focus is on the structure of a middleware for the synchronization of the CPS and its virtual representation while accessing big data. The digital twin contains functional and behavioral models that are activated when the CPS logs into the centralized support architecture. Communication between CPS and the digital representative is enabled by a WebSocket channel. If the CPS disconnects from the support architecture, the digital twin and all its components are deactivated. Within the research project AUTOWARE, an eponymous cognitive digital automation operation system was developed [66]. The framework includes a reference architecture, in which Digital Twins of (smart) products are included. According to the authors, AUTOWARE can support the efficient development and operation of cognitive manufacturing systems. The used digital twin is an extension of the software architecture developed in the project ReconCell [67]. Within ReconCell, a set of components for a robot workstation for automated assembly tasks is developed. One of those components is a Digital Twin of the work cell. The DT is based on the commercial 3D simulation software VEROSIM. [PERSON] et al. divided the DTs of subjects participating in the manufacturing context into a hierarchical model [68]. There are DTs for single components such as machines, material or equipment at unit level and DTs for production line, complex products or the shop floor at system level. Through interoperability and dependencies in cooperated applications and collection data over the whole life-cycle the system level DTs build up a SoS DT. Therefore, the DTs \"co-evolve over the lifecycle of the product process.\" According to the authors, models play an important role for DTs to interpret and predict behavior. Since different models exists in deeper unit level for each subject, all of them have to be combined and integrated by the DT at the system level. The same challenge exists for DTs at SoS level with system DT models. As the authors of [52; 69; 37] provided more extensive surveys on recent developments in the area of digital twins for manufacturing, we proceed with highlighting key enabling technologies for modeling digital twins, as presented recently by [PERSON] et al. [70]. The authors clustered those key enabling technologies into five categories and conducted a survey on the state of the art in five categories: physics-based modeling, data-driven modeling, big data cybernetics, infrastructure and platforms and human-machine interface. Technologies for physics-based modeling tackle aspects of how to translate theories developed through observation of physical phenomena into mathematical equations and how to solve them. Examples for such technologies are 3D modeling and simulation techniques such as those presented in [71] and numerical solvers that are already integrated into numerical simulators such as the open-source software OpenFOAM that allows simulating fluid dynamics [72].