Dimension Reduction and Breakdown of Recurrent Neural Networks in the context of Multiscale Analyses

Once properly trained, artificial Neural Networks can serve as surrogate model of non-linear history-dependent micro-scale boundary value problems in multi-scale methods. This paradigm has been essentially used as a mapping between the macro-stress and macro-strain tensors of the micro-scale boundary value problem and the micro-structure information could not be recovered in a so-called localization step. However such information can be of interest in order to assess failure or fatigue, e.g. In this paper, we present a Recurrent Neural Networks (RNNs)-based surrogate of the micro-scale boundary value problem, while being able to recover the evolution of the local micro-structure fields. In order to address the curse of dimensionality arising because of the large amount of internal state variables defining the micro-structure, PCA dimension reduction and dimension break down, i.e. the use of several RNNs instead of a single one, are combined to reduce the size of the different RNNs that have to be trained. We show that RNNs can be used to conduct multi-scale simulations of heterogeneous elasto-plastic structures while micro-scale information can be recovered during a post-simulation localization step.