In industry, there is a high interest in assembly simulations involving flexible surface-like and flexible volumetric components. The overall goal is to make realistically behaving models of such deformable structures available for interactive handling in virtual or augmented, i.e. extended reality (XR). This could be achieved by physics-based simulation technology and mathematical methods for nonlinear model order reduction in combination with databased modelling and artificial intelligence (AI). Speeding up simulations by methods of this type is necessary since the physics-based simulation models in focus belong to the class of geometrically nonlinear structural models, such that standard methods of computational structural mechanics are far too costly to achieve the performance necessary for simulations at interactive frame rates. The joint research activities of ITWM and FCC investigate the potential of nonlinear model order reduction (nl-MOR) techniques [1], complemented by methods utilizing AI-based surrogate modelling to speed-up specific algorithmic parts of an nl-MOR method, or, alternatively, provide an inherently different algorithmic approach based on machine learning methods [2] to estimate the outcome of mechanical equilibrium computations (including error estimates) with utmost computational performance. In our presentation we will outline our research program and show first results.