The Industrial Metaverse is a space to experience the Digital Twin (DT) of industrial assets like products, machines, systems, plants or infrastructures. The experience is characterized by immersive visualization, real-time interaction, and the possibility to collaborate. Metaverse applications can support the operation phase with the intuitive (remote) monitoring and performance prediction of complex technical systems such as factories, buildings or urban infrastructure through the use of novel human-DT interaction interfaces. Similarly, metaverse based simulations can also focus on the engineering phase of a product, where they can provide instant intuitive feedback on design changes, while enabling a collaborative simultaneous analysis of such feedback. Key enabler for these and similar applications are technologies for fast simulation of the behavior of the physical assets. To realize real-time interaction, it is necessary that the Digital Twin not only describes the current state of the asset, e.g., by visualization of on-line and historic data, but also predicts its future behavior in real-time. In general, the different methods for fast simulation distinguish themselves in the need of models and/ or data. Their applicability strongly depends on the requirements with respect to accuracy, execution time, scalability and the capability to extrapolate and predict. One popular method is the use of neural networks to learn the behavior of the assets from measurement or artificial (e.g., simulated) data. Whereas this method is well-established in situations where the operation scenario is well-known and data is already available, its application for previously unknown situations is limited. Physics-based simulation models on the other hand are well-established in engineering in the early design stages and can predict with high accuracy. However, these models require powerful hardware and are typically unable to run in real time. So-called model order reduction (MOR) methods can transform these models into real-time-capable Digital Twins and are one means to speed up these models for real-time applications while maintaining their extrapolation capability. In our talk, we will present an overview of the aforementioned technologies and show how they can support the industrial metaverse based on industrial examples.