Self-consistency Reinforced Recurrent Neural Networks acting as surrogates of highly-nonlinear composite responses in multi-scale simulations

Data-driven approaches allow accelerating multi-scale simulations: the micro-scale problem resolution is substituted by a surrogate model trained from off-line simulations. In the context of history-dependent materials, recurrent neural networks can act as such a surrogate, see e.g. [1], since their hidden variables allow accounting for irreversible behaviours.
This however requires a training dataset that virtually covers all the possible strain-stress state evolutions encountered during the online phase. This dataset size can thus become prohebitive in particular when the strain increment size is expected to vary by several orders of magnitude. This is typically the case for highly non-linear problems such as the ones involving damage and or fracture since the time step size can be reduced during the on-line stage. 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.
Nevertheless, when considering a composite representative volume element response in the context of multi-scale simulations, a Self-Consistent recurrent network 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 highly nonlinear multi-scale simulations, including in the case of damage and fracture.
This project has received funding from the European Union’s Horizon Europe Framework Programme under grant agreement No. 101056682 for the project ‘‘DIgital DEsign strategies to certify and mAnufacture Robust cOmposite sTructures (DIDEAROT)’’. The contents of this publication are the sole responsibility of ULiege and do not necessarily reflect the opinion of the European Union. Neither the European Union nor the granting authority can be held responsible for them.
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”, Comp. Meth. in Appl. Mech. and Engng. Vol. 369, p. 113234, (2020)
[2]
C. Bonatti, D. Mohr, “On the importance of self-consistency in recurrent neural network models representing elasto-plastic solids”, J. of the Mech. and Phys. of Sol. Vol. 158, p. 104697 (2022)
[3]
L. Wu and L. Noels, “Self-consistency Reinforced minimal Gated Recurrent Unit for surrogate modelling of history dependent non-linear problems: Application to history-dependent homogenized response of heterogeneous materials”, Comp. Meth. in Appl. Mech. and Engng., Vol. 424, p. 116881, (2024).