In recent years, model order reduction (MOR) techniques have been developed to speed up finite element (FE) simulations, particularly when fast online calculations are required. This is especially true for digital twins, where real-time simulations are essential. Most of the reduction methods are implemented for classical FE. In many instances, different FE formulations are advantageous; however, the applicability of reduced order models (ROMs) in these variations has not been investigated in depth. An example is the unfitted domain methods, where the physical domain is decoupled from the discretization solution. One such technique is the immersed isogeometric analysis (IGA) [1], for which a ROM framework was introduced in [2]. Similar to immersed IGA, the finite cell method (FCM) [3] combines high order elements with unfitted domain discretizations. Even for complex geometries, FCM generates a simple structured mesh and a solution with high convergence rates, avoiding the time-consuming meshing process without sacrificing accuracy. Additionally, given the nature of the FC discretization, the same underlying mesh can be used for multiple geometries. As a result, the system and solution vector dimensions remain constant, eliminating the need to manipulate the matrices during the reduction stage to address the dimension mismatch inherent to other techniques when the geometry changes. In this work, both intrusive and non-intrusive MOR techniques are evaluated for FCM to accelerate the simulations. Furthermore, we investigate the accuracy and limitations of the approximations, as well as the influence of the FCM parameters on the ROMs. Additionally, the results are compared to those obtained with classical FE formulations. References [1] D. Schillinger et al. An isogeometric design-through-analysis methodology based on adaptive hierarchical refinement of NURBS, immersed boundary methods, and T-spline CAD surfaces, Comput. Methods Appl. Mech. Engrg. 249 (2012) 116–150. https://doi.org/10.1016/j.cma.2012.03.017. [2] M. Chasapi et al. A localized reduced basis approach for unfitted domain methods on parameterized geometries, Comput. Methods Appl. Mech. Eng. 410 (2023) 115997. https://doi.org/10.1016/j.cma.2023.115997 [3] J Parvizian et al. Finite cell method. Comput Mech 41, 121–133 (2007). https://doi.org/10.1007/s00466-007-0173-y