  This work is the first to employ and adapt the image-to-image translation
concept based on conditional generative adversarial networks (cGAN) towards
learning a forward and an inverse solution operator of partial differential
equations (PDEs). Even though the proposed framework could be applied as a
surrogate model for the solution of any PDEs, here we focus on steady-state
solutions of coupled hydro-mechanical processes in heterogeneous porous media.
Strongly heterogeneous material properties, which translate to the
heterogeneity of coefficients of the PDEs and discontinuous features in the
solutions, require specialized techniques for the forward and inverse solution
of these problems. Additionally, parametrization of the spatially heterogeneous
coefficients is excessively difficult by using standard reduced order modeling
techniques. In this work, we overcome these challenges by employing the
image-to-image translation concept to learn the forward and inverse solution
operators and utilize a U-Net generator and a patch-based discriminator. Our
results show that the proposed data-driven reduced order model has competitive
predictive performance capabilities in accuracy and computational efficiency as
well as training time requirements compared to state-of-the-art data-driven
methods for both forward and inverse problems.
