Parametrized non intrusive space-time approximation for explicit dynamic fem applications

In the following work, a benchmark of different non-intrusive model reduction approaches is performed on an explicit dynamic contact 3D-problem. The main purpose of this work is to evaluate the stability of the reduced model with respect to time along with the precision of these approaches with respect to the true solutions of interest. These solutions are the prediction of displacement and velocity fields. The precision of these approaches is also evaluated with respect to the evolution of some materials parameters. Six parameters vary in this study and we would like to predict the whole transient fast dynamic impact response with respect to each parameters. To this end, several models are trained : Proper Orthogonal Decomposition (POD) and Deep convolutional Neural Network (DcNN), in addition, a vectorized version of Interpolation in Grassman Manifolds is proposed. The benchmark performed illustrate that using DcNN’s allows to achieve the best precision and stability in predicting physical fields.