  Digital twins have emerged as a key technology for optimizing the performance
of engineering products and systems. High-fidelity numerical simulations
constitute the backbone of engineering design, providing an accurate insight
into the performance of complex systems. However, large-scale, dynamic,
non-linear models require significant computational resources and are
prohibitive for real-time digital twin applications. To this end, reduced order
models (ROMs) are employed, to approximate the high-fidelity solutions while
accurately capturing the dominant aspects of the physical behavior. The present
work proposes a new machine learning (ML) platform for the development of ROMs,
to handle large-scale numerical problems dealing with transient nonlinear
partial differential equations. Our framework, mentioned as
$\textit{FastSVD-ML-ROM}$, utilizes $\textit{(i)}$ a singular value
decomposition (SVD) update methodology, to compute a linear subspace of the
multi-fidelity solutions during the simulation process, $\textit{(ii)}$
convolutional autoencoders for nonlinear dimensionality reduction,
$\textit{(iii)}$ feed-forward neural networks to map the input parameters to
the latent spaces, and $\textit{(iv)}$ long short-term memory networks to
predict and forecast the dynamics of parametric solutions. The efficiency of
the $\textit{FastSVD-ML-ROM}$ framework is demonstrated for a 2D linear
convection-diffusion equation, the problem of fluid around a cylinder, and the
3D blood flow inside an arterial segment. The accuracy of the reconstructed
results demonstrates the robustness and assesses the efficiency of the proposed
approach.
