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This work aims to interpolate parametrized Reduced Order Model (ROM) basisconstructed via the Proper Orthogonal Decomposition (POD) to derive a robustROM of the system's dynamics for an unseen target parameter value. A novelnon-intrusive Space-Time (ST) POD basis interpolation scheme is proposed, forwhich we define ROM spatial and temporal basis \emph{curves on compact Stiefelmanifolds}. An interpolation is finally defined on a \emph{mixed part} encodedin a square matrix directly deduced using the space part, the singular valuesand the temporal part, to obtain an interpolated snapshot matrix, keeping trackof accurate space and temporal eigenvectors. Moreover, in order to establish awell-defined curve on the compact Stiefel manifold, we introduce a newprocedure, the so-called oriented SVD. Such an oriented SVD produces uniqueright and left eigenvectors for generic matrices, for which all singular valuesare distinct. It is important to notice that the ST POD basis interpolationdoes not require the construction and the subsequent solution of areduced-order FEM model as classically is done. Hence it is avoiding thebottleneck of standard POD interpolation which is associated with theevaluation of the nonlinear terms of the Galerkin projection on the governingequations. As a proof of concept, the proposed method is demonstrated with theadaptation of rigid-thermoviscoplastic finite element ROMs applied to a typicalnonlinear open forging metal forming process. Strong correlations of the ST PODmodels with respect to their associated high-fidelity FEM counterpartsimulations are reported, highlighting its potential use for near real-timeparametric simulations using off-line computed ROM POD databases.

A Non-Intrusive Space-Time Interpolation from Compact Stiefel Manifolds of Parametrized Rigid-Viscoplastic FEM Problems