Summary: In continuum mechanics, the prediction of defect harmfulness requires to solve approximately partial differential equations with given boundary conditions. In this contribution boundary conditions are learnt for tight local volumes (TLV) surrounding cracks in three-dimensional volumes. A nonparametric data-driven approach is used to define the space of defects, by considering defects observed via X-Ray computed tomography. The dimension of the ambient space for the observed images of defects is huge. A nonlinear dimensionality reduction scheme is proposed in order to train a reduced latent space for both the morphology of defects and their local mechanical effects in the TLV. A multimodal autoencoder enables to mix morphological and mechanical data. It contains a single latent space, termed mechanical latent space. But this latent space is fed by two encoders. One is related to the images of defects and the other to mechanical fields in the TLV. The latent variables are input variables for a geometrical decoder and for a mechanical decoder. In this work, mechanical variables are displacement fields. The autoencoder on mechanical variables enables projection-based model order reduction as proposed in the study of Lee and Carlberg. The main novelty of this paper is a submodeling approach assisted by artificial intelligence. Here, for defect images in the test set, Dirichlet boundary conditions are applied to TLV. These boundary conditions are forecasted by the mechanical decoder with a latent vector predicted by the morphological encoder. For that purpose, a mapping is trained to convert morphological latent variables into mechanical latent variables, denoted “direct mapping.” An “inverse mapping” is also trained for error estimation with respect to morphological predictions. Errors on mechanical predictions are close to 5% with simulation speed-up ranging for 3 to 120. We show that latent variables forecasted by the images of defects are prone to a better understanding of the predictions.
{© 2021 John Wiley & Sons, Ltd.}