Continuous conditional generative adversarial networks for data-driven solutions of poroelasticity with heterogeneous material properties

Machine learning-based data-driven modeling can be computationally efficient solutions of time-dependent subsurface geophysical systems. In this work, our previous approach of conditional generative adversarial networks (cGAN) developed for steady-state problems with heterogeneous materials is extended to time-dependent problems by adopting the concept of continuous cGAN (CcGAN). The CcGAN that can condition continuous variables in the cGAN framework is developed to incorporate the time domain through either element-wise addition or conditional batch normalization. As a demonstration case, the transient response of the coupled poroelastic process is studied in two different permeability fields: Zinn \& Harvey transformation and a bimodal transformation. The proposed CcGAN uses heterogeneous permeability fields as input parameters while pressure and displacement fields over time are model output. Our results show that the model provides sufficient accuracy with computational speed-up. This robust framework will enable us to perform real-time reservoir management and robust uncertainty quantification in realistic problems.