  This work aims to interpolate parametrized Reduced Order Model (ROM) basis
constructed via the Proper Orthogonal Decomposition (POD) to derive a robust
ROM of the system's dynamics for an unseen target parameter value. A novel
non-intrusive Space-Time (ST) POD basis interpolation scheme is proposed, for
which we define ROM spatial and temporal basis \emph{curves on compact Stiefel
manifolds}. An interpolation is finally defined on a \emph{mixed part} encoded
in a square matrix directly deduced using the space part, the singular values
and the temporal part, to obtain an interpolated snapshot matrix, keeping track
of accurate space and temporal eigenvectors. Moreover, in order to establish a
well-defined curve on the compact Stiefel manifold, we introduce a new
procedure, the so-called oriented SVD. Such an oriented SVD produces unique
right and left eigenvectors for generic matrices, for which all singular values
are distinct. It is important to notice that the ST POD basis interpolation
does not require the construction and the subsequent solution of a
reduced-order FEM model as classically is done. Hence it is avoiding the
bottleneck of standard POD interpolation which is associated with the
evaluation of the nonlinear terms of the Galerkin projection on the governing
equations. As a proof of concept, the proposed method is demonstrated with the
adaptation of rigid-thermoviscoplastic finite element ROMs applied to a typical
nonlinear open forging metal forming process. Strong correlations of the ST POD
models with respect to their associated high-fidelity FEM counterpart
simulations are reported, highlighting its potential use for near real-time
parametric simulations using off-line computed ROM POD databases.
