Enabling parametric ROMs with LRTD
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The space-time-parameter structure of parametric dynamical systems calls for the application of tensor methods to construct reduced-order models (ROMs). In a tensor-based ROM framework, traditional dimension reduction techniques, such as matrix SVD, extend to low-rank tensor decomposition (LRTD). This extension of Galerkin-based POD ROMs using tensors enhances both the practical efficiency of the ROM and its suitability for error analysis in parametric systems. In this work, I will present the new LRTD-ROM framework, discuss the available analysis, and demonstrate the capabilities of tensor methods in reducing model complexity.
