Self-consistency Reinforced Recurrent Neural Networks to accelerate visoelasto-viscoplastic multi-scale problems

Multi-scale simulations are accelerated using data-driven approaches. In that context the micro-scale problem resolution is substituted by a surrogate trained from off-line simulations performed on Representative Volume Element (RVE). In the context of history-dependent materials, recurrent neural networks have widely been considered to act as such a surrogate, see e.g. [1], since their hidden variables allows accounting for the history. However, defining a dataset for the training which virtually covers all the possible strain-stress state evolution encountered during the online phase remains a daunting task, in particular when the strain increment size is expected to vary by several orders of magnitude. Self-Consistent recurrent networks were thus introduced in [2] to reinforce the objectivity of the neural network predictions with respect to the strain increment size.
This new cell was applied to substitute an elasto-plastic material model. Nevertheless, when
considering a RVE response in the context of multi-scale simulations, a Self-Consistent recurrent networks might require a long training process. We have thus revisited the Self-Consistent recurrent unit in order to improve the training performance and reduce the number of trainable variables for the neural network to act as a composite surrogate model in multi-scale simulations.
[1] L. Wu, V. D. Nguyen, N. G. Kilingar, L. Noels, A recurrent neural network-accelerated multi-scale model for elasto-plastic heterogeneous materials subjected to random cyclic and non-proportional loading paths, Computer Methods in Applied Mechanics and Engineering 369 (2020) 113234. doi: https://doi.org/10.1016/j.cma.2020.113234
[2] C. Bonatti, D. Mohr, On the importance of self-consistency in recurrent neural network models representing elasto-plastic solids, Journal of the Mechanics and Physics of Solids 158 (2022) 104697. doi: https://doi.org/10.1016/j.jmps.2021.104697
[3] L. Wu, L. Noels, L. Wu and L. Noels. Self-consistency Reinforced minimal Gated Recurrent Unit for surrogate modeling of history-dependent non-linear problems: Application to history-dependent homogenized response of heterogeneous materials." Computer Methods in Applied Mechanics and Engineering, 424 (01 May 2024): 116881. doi: https://doi.org/10.1016/j.cma.2024.116881