A Self-consistent Reinforced minimal Gated Recurrent Unit for surrogate modelling of elasto-plastic multi-scale problems

editorial reviewed
Multi-scale simulations can be accelerated by substituting the micro-scale problem resolution by a surrogate trained from off-line simulations. In the context of history-dependent materials, recurrent neural networks have widely been considered to act as such a surrogate, e.g. [1], since their hidden variables allow for a memory effect.However, defining a training dataset which virtually covers all the possible strain-stress state evolution encountered during the online phase remains a daunting task. This is particularly true in the case in which 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 self-consistency of neural network predictions when small strain increments are expected. This new cell was applied to substitute an elasto-plastic material model. However when considering a representative volume element response in the context of multi-scale simulations, it was found that the Self-Consistent recurrent networks requires a long training process. In this work, we revisit the Self-Consistent recurrent unit 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.This project has received funding from the European Union’s Horizon Europe research and innovation programme under grant agreement No. 101056682.REFERENCES[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 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:10.1016/j.cma.2024.116881
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