[en] Artificial Neural Networks (NNWs) are appealing tools to serve as surrogate model
of high dimensional and non-linear history-dependent problems in computational mechanics, in particular in multi-scale methods. Indeed, as shown in  once properly
trained, they replace expensive micro-scale finite element resolutions allowing reducing
the computational time by more than 4 orders of magnitude.
Nevertheless, such a paradigm is essentially used as a mapping between the macro-stress
and macro-strain tensors of the micro-scale boundary value response and the micro-structure information could not be recovered in a so-called localization step.
In this talk, 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 state variables for complex loading scenarios . In order to
address the curse of dimensionality arising because of the large amount of internal
state variables in the micro-structure, we enrich the RNN with PCA dimension reduction
and dimension break down, i.e. the use of several RNNs instead of a single one.
Besides, the sequential training strategy is optimized in order to allow for GPU usage.
 L. Wu, V.-D. Nguyen, N.G. Kilingar and L. Noels, Computer Methods in Applied
Mechanics and Engineering, 360:113234, 2020.
 L. Wu, L. Noels, Recurrent Neural Networks (RNNs) in computational mechanics
for high dimensional problems: RNNs structure design through dimension reduction
and break down; application to multi-scale localization step. Submitted.
Wu, Ling ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Computational & Multiscale Mechanics of Materials (CM3)
Noels, Ludovic ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Computational & Multiscale Mechanics of Materials (CM3)
Recurrent Neural Networks (RNNs) with dimension reduction and break down in the context of high dimensional localization step in multi-scale analysis
Publication date :
04 April 2022
Event name :
18th European Mechanics of Materials Conference (EMMC18)
Event organizer :
Event place :
Oxford, United Kingdom
Event date :
4-6 April 2022
European Projects :
H2020 - 862015 - MOAMMM - Multi-scale Optimisation for Additive Manufacturing of fatigue resistant shock-absorbing MetaMaterials
Name of the research project :
EC - European Commission
Funding number :
Funding text :
This project has received funding from the European Union´s Horizon 2020 research and innovation programme under grant agreement No. 862015 for the project “Multiscale Optimisation for Additive Manufacturing of fatigue resistant shock-absorbing MetaMaterials (MOAMMM)” of the H2020-EU.1.2.1. - FET Open Programme.