Towards Purely Parameter-Specific Model Order Reduction: A Tensor Decomposition-Based Approach

In the context of digital twins, projection-based model order reduction (MOR) plays a crucial role in real-time control, fault diagnosis and performance prediction, particularly when accounting for multi-parameter variations in complex systems. However, traditional MOR techniques often exhibit limited robustness to such variations. This limitation arises from the fact that parameter information is typically not embedded in the construction of the reduced basis, resulting in models that lack parametric specificity. This work presents a comprehensive comparison between a tensor decomposition-based MOR method (TDMOR) and three representative MOR approaches, namely classical proper orthogonal decomposition (POD), ideal local POD, and block POD, using a four-parameter surrogate modeling of an electric motor. Numerical results demonstrate that employing more localized snapshots improves the robustness of the reduced basis to parameter variations, thereby enhancing the accuracy of the reduced model. The proposed TDMOR approach closely approximates the performance of ideal local POD without requiring a large number of pre-stored local bases, making it an effective solution for nonlinear, multi-parameter systems.