## 3 Design of a Hybrid and Distributed Digital Twins Model for Industrial Scenarios
The DT model crafted by IoTwins utilizes big data and domain expert knowledge to depict a complex system (such as an industrial plant, process, or facility) along with its application-specific performance indicators. The ambition is to accurately predict the temporal evolution and dynamics of the system. Conceptually, IoTwins envisions the development of the following DT types: _simulation-based_, employing either agent-oriented knowledge or agent-oriented knowledge. The DT model crafted by IoTwins utilizes big data and domain expert knowledge to depict a complex system (such as an industrial plant, process, or facility) along with its application-specific performance indicators. The ambition is to accurately predict the temporal evolution and dynamics of the system. Conceptually, IoTwins envisions the development of the following DT types: _simulation-based_, employing either agent-oriented knowledge or agent-oriented knowledge. The ambition is to accurately predict the temporal evolution and dynamics of the system. Conceptually, IoTwins envisions the development of the following DT types: _simulation-based_, employing either agent-oriented knowledge or agent-oriented knowledge. modeling or physical modeling; _data-driven_, utilizing cutting-edge ML/DL techniques; _hybrid_, combining the strengths of both physics and data modeling. A sample hybrid DT was developed in Test-bed 3. Here, in the aim of developing a predictive model of a machine part's faults, a ML model was implemented and trained with real-time data gathered from the sensors on board on the machine part. Given the scarcity of data sensed when the component ran in a near-to-faulty mode, the manufacturing company had to resort to simulation in order to generate synthetic data related to the malfunctioning of the part. Such data were then used along with real data to train a robust ML model for the prediction purpose. Furthermore, in order to cater for the computing needs of factories, as well as for the strict requirements of certain types of industrial applications, IoTwins fosters a _hierarchical distribution_ and interworking of DTs that includes: (i) _IoT Twins_, which employ lightweight models of specific components, and conduct big-data processing and local control for quality management operations with a focus on low latency and high reliability; (ii) _Edge Twins_, situated at plant gateways, which offer higher-level control functionalities and orchestrate Internet of Things (IoT) sensors and actuators within a production locality. This facilitates local optimizations and promotes interoperability; (iii) _Cloud Twins_, which engage in time-consuming, typically off-line parallel simulation and deep-learning processes. They provide the edge twin with pre-elaborated predictive models, efficiently executed at production plant premises for monitoring, control, and tuning purposes. From a methodological perspective, the whole DT model definition process envisaged two iterations: in the first iteration, requirements elicited from the industrial manufacturing and facility management IPs (say \"group A\") were used to design a first draft of the DT model, which was then prototyped in collaboration with the scientific partners and validated on the test-beds owned by _group A_ IPs; in the second iteration, results collected from the mentioned experiments and new requirements elicited from the so-called replicability IPs (say \"group B\") contributed to refining the DT model, which was eventually validated on a second set of test-beds owned by _group B_ IPs. Finally, in Figure 1, we depict a graphical representation of the hybrid and distributed DT model developed within the IoTwins project. First, a DT (illustrated as a blue-filled box) is a distributed entity with the potential to encompass the entire spectrum of an industrial scenario. This spans from the remote Cloud down to the factory premises, where it can operate on Edge nodes and on field devices/PLC (labeled as \"IoT\").