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Title: Operator learning for homogenizing hyperelastic materials, without PDE data
In this work, we address operator learning for stochastic homogenization in nonlinear elasticity. A Fourier neural operator is employed to learn the map between the input field describing the material at fine scale and the deformation map. We propose a variationally-consistent loss function that does not involve solution field data. The methodology is tested on materials described either by piecewise constant fields at microscale, or by random fields at mesoscale. High prediction accuracy is obtained for both the solution field and the homogenized response. We show, in particular, that the accuracy achieved with the proposed strategy is comparable to that obtained with the conventional data-driven training method.  more » « less
Award ID(s):
2022040
PAR ID:
10539887
Author(s) / Creator(s):
;
Publisher / Repository:
Science Direct
Date Published:
Journal Name:
Mechanics Research Communications
Volume:
138
Issue:
C
ISSN:
0093-6413
Page Range / eLocation ID:
104281
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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