Abstract
Reduced order models (ROMs) are employed, to approximate the high-fidelity solutions while accurately capturing the dominant aspects of the physical behavior. In this work, a non-intrusive ROM is employed to reduce the computational cost and provide numerical solutions in a limited amount of time. The utilized framework, mentioned as FastSVD-ML-ROM applies (i) a singular value decomposition (SVD) update methodology to compute a linear subspace of the high-fidelity solutions during the simulation process, (ii) convolutional autoencoders for nonlinear dimensionality reduction, (iii) feed-forward neural networks to map the input parameters to the latent spaces, and (iv) long short-term memory networks to predict the dynamics of parametric solutions. The efficiency of the FastSVD-ML-ROM is demonstrated both for the Navier stokes equation in the frame of fluid dynamics and for the Navier-Cauchy equations dealing with structural dynamics. In particular, the developed framework is used to monitor the flow field around a cylinder in real-time and for the wave propagation on aluminum plates targeting to evaluate the effect of the uncertainties introduced in the material properties. The accuracy of the predicted results compared to the high-fidelity solutions showcase the robustness of the proposed approach.