## 3 State of the Art in Digital Twins and Cyber-Ranges
### State of the Art in Digital Twins
Data-driven modeling aims for the identification of patterns in large datasets, assuming that the data already encode information on physical phenomena. Enabling technologies include data generation techniques (e.g., crowd-based data gathering [73]), data privacy solutions [74], machine learning algorithms [75; 76] and artificial intelligence approaches such as generative adversarial networks for denoising images [77]. Such techniques allow reducing the difference between real operational situation the real system is facing and the interpreted situation that the digital twin creates by sensor data of its physical counterpart. Big data cybernetics [78] merges control theory with big data and aims for steering the system to a given state. From control theory perspective, the behavior of the system is constantly monitored and the evolution is compared to the reference state. Big data approaches are used for increasing the understanding of the observations, which can be used for improving controller performance for the digital twin and its physical counterpart. Examples for such big data approaches are filtering techniques [79] and reduced ordering modeling [80], both aiming for identifying what is relevant in the dataset. Enabling technologies of digital twins in the area of infrastructure and platforms include IoT, cloud computing and 5G (see [70] for a list of approaches and commercial services in this area). The increasing use of DTs in the several fields previously described led to the emergence of several software solutions dedicated to the DT implementation. As what happens with the definition of DT, usually, those software solutions are designed taking into account just the functionality that is needed in some moment for specific applications and the specific chosen definition for a DT. For this reason, the main software solutions are proprietary solutions designed by each player to accomplish the need of their product. There are many commercial software solutions that implement industrial DT technology, mainly developed by big companies of the manufacturing sector. The following is a non-exhaustive list of popular vendor DT technologies:  
* General electric (GE) developed an advanced and functional Digital Twin that integrates analytic models for components of the power plant that measure asset health, wear and performance. This DT can be integrated into the GE developed distributed prefix platform for \"large-scale machine data processing, management and analytics\" and IIoT applications [81]. * PTC Windchill is a DT developed by PTC to help manufacturers across industries understanding how their customers are using their products. This way, they can help them to improve the design and performance of those products [82]. * 3 DS is a DT developed by Dassault Systemes that allows manufacturers to make virtual products available to the market for experimentation and testing in realistic conditions before engaging in any real production [83]. * Microsoft Azure DT Software is an IoT service that virtually replicates the physical world by modeling the relationships among people, places and devices in a spatial intelligence graph [84]. * Seebo DT is a graphical interface that allows the generation of actionable insights that maximize overall equipment effectiveness, reduce unplanned downtime and uncover the root cause of issues. Dashboards allow real-time visualization of the operational health of deployed machines and display enriched alerts with predictive metrics based on key machine parameters, such as machine temperature, pressure, vibration, humidity, fatigue and wear in order to quickly identify and solve issues remotely [85]. * Anylogic software provides simulation capabilities in a single commercial package with special research licenses available. It is specialized in factories and production lines, with discrete-event simulation capabilities, and has libraries capable of supporting several types of fields [86].