  The analysis of parametric and non-parametric uncertainties of very large
dynamical systems requires the construction of a stochastic model of said
system. Linear approaches relying on random matrix theory and principal
componant analysis can be used when systems undergo low-frequency vibrations.
In the case of fast dynamics and wave propagation, we investigate a random
generator of boundary conditions for fast submodels by using machine learning.
We show that the use of non-linear techniques in machine learning and
data-driven methods is highly relevant.
  Physics-informed neural networks is a possible choice for a data-driven
method to replace linear modal analysis. An architecture that support a random
component is necessary for the construction of the stochastic model of the
physical system for non-parametric uncertainties, since the goal is to learn
the underlying probabilistic distribution of uncertainty in the data.
Generative Adversarial Networks (GANs) are suited for such applications, where
the Wasserstein-GAN with gradient penalty variant offers improved convergence
results for our problem.
  The objective of our approach is to train a GAN on data from a finite element
method code (Fenics) so as to extract stochastic boundary conditions for faster
finite element predictions on a submodel. The submodel and the training data
have both the same geometrical support. It is a zone of interest for
uncertainty quantification and relevant to engineering purposes. In the
exploitation phase, the framework can be viewed as a randomized and
parametrized simulation generator on the submodel, which can be used as a Monte
Carlo estimator.
