## 4 Challenges
### Optimization Challenges  
Realizing a DT in CPS that accounts for the interactions of computing, control, communication, and data analysis modules in an end-to-end chain is challenging. The communication resource allocation algorithms, such as time and frequency resource scheduling, are very complex, especially when combined with massively distributed networking devices and low latency requirements. In addition, the computing resource allocation, such as task-offloading in an edge/cloud computing architecture, is another optimization problem with stringent performance constraints. Furthermore, the control mechanism, possibly event-triggered or time-triggered control, or both, yields still another optimization problem. In addition, analysis of the collected data is highly complex, requiring prodigious feature extraction, and training (or at least validation), coupled with potentially continual prediction or classification to satisfy real-time requirements. The DT is a combination of the real-time computing, real-time control, and real-time communication, which generates the joint/integrated optimization problem of computing, control, and communication. Consider VR-supported smart manufacturing as an example. First, we need to deliver massive amounts of sensing data with required latency. Then, we need to use the graphics engine to generate the digital model in real time. Finally, we need to execute the control command within the latency constraint. Since any problem in this chain will directly affect the performance of the other, even in a centralized system with superior hardware conditions, it is very challenging to perform joint optimization on this VR system. Further, the distributed system of CPS only makes the problem of joint optimization much harder. For example, in our previous work [105], we adopted deep reinforcement learning to help configure the network and dynamically change the sensor sampling rate at the same time to improve the control performance of a distributed smart manufacturing system. However, by introducing DT to the CPS, there are more processes that need to be considered. For example, in the control process, there are two processes, such as the domain expert controlling DT and DT controlling the physical objects. The computing of DT in CPS needs to consider three computing processes, such as the computing process of generating a digital copy of a physical object, the computing process of the interaction between DTs in a simulated scenario, and the computing process of actual CPS tasks. The communication of DT in CPS needs to consider the communication between the physical object and the virtual clone, the communication between the DT and other DTs, and the communication between the DT and the human control interface. These extra processes make the optimization problem more difficult to solve. Taking into account the limited resources of the CPS system, we also need to optimize the large amount of data generated in these processes from the perspective of data generation, data storage, and data transmission. From a data generation perspective, when we generate the data needed to build a DT in CPS, the quality of the data is a major issue. Because we need to deploy a massive number of CPS devices, the hardware conditions of a single CPS device are often very limited. In addition, in the CPS environment, one type of data may be collected by multiple sources. Thus, how to effectively select data sources for different CPS applications is a challenging problem. From a data storage perspective, when we are building the DT, in order to truly reflect the timely update of physical objects, we often sample the state of physical objects at a relatively high frequency. Inevitably, an incredible volume of data will be collected on the DT server side. On one hand, these data can be used to assist in the development of other DT systems; on the other hand, these data take up significant storage space.