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The aim of the present study is to analyse and predict the structural deformations occurring during shock tube experiments with a series of recurrent and temporal convolutional neural networks. The goal is to determine the architecture that can best learn and predict physically and geometrically nonlinear deformations. For this approach, four different architectures are proposed. Firstly, the multi-layered long-short term memory is developed followed by the multi-layered gated recurrent unit (GRU). Both the RNNs allow accounting for history dependent behaviors through their corresponding internal variables. Further, a multilayered temporal convolutional network is initialized, where the dilated convolution operation is responsible for tracing the path dependent behavior. In the mentioned architectures a sequence of mechanical data is passed through the network and a transformation to corresponding displacements is established. These sequences and corresponding deflections belong to a wide range of strain rates in the dynamic response of structures consisting of steel, aluminum, and copper plates including geometrical and physical non-linearities. Finally, an encoder–decoder architecture consisting of GRU layers is introduced with a modified attention mechanism which showed the best result for predicting the dynamic response. Employing comparative calculations between the neural network (NN) enhanced predictions and the measurements, the nature of approximation of each mentioned NN architecture is discussed and the capabilities of these developed surrogate models are demonstrated by its prediction on validation experiments. These validation experiments have displacement and input data ranges beyond the range of data used for training the aforementioned models.