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This work is the first to employ and adapt the image-to-image translationconcept based on conditional generative adversarial networks (cGAN) towardslearning a forward and an inverse solution operator of partial differentialequations (PDEs). Even though the proposed framework could be applied as asurrogate model for the solution of any PDEs, here we focus on steady-statesolutions of coupled hydro-mechanical processes in heterogeneous porous media.Strongly heterogeneous material properties, which translate to theheterogeneity of coefficients of the PDEs and discontinuous features in thesolutions, require specialized techniques for the forward and inverse solutionof these problems. Additionally, parametrization of the spatially heterogeneouscoefficients is excessively difficult by using standard reduced order modelingtechniques. In this work, we overcome these challenges by employing theimage-to-image translation concept to learn the forward and inverse solutionoperators and utilize a U-Net generator and a patch-based discriminator. Ourresults show that the proposed data-driven reduced order model has competitivepredictive performance capabilities in accuracy and computational efficiency aswell as training time requirements compared to state-of-the-art data-drivenmethods for both forward and inverse problems.

A framework for data-driven solution and parameter estimation of PDEs using conditional generative adversarial networks