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

TL;DR

This paper introduces a continuous conditional GAN framework for efficiently solving time-dependent poroelasticity problems with heterogeneous materials, enabling real-time predictions and handling variable data timestamps.

Contribution

The work extends previous steady-state cGANs to time-dependent problems by incorporating continuous variables like time, enhancing flexibility and applicability to complex subsurface simulations.

Findings

Accurately predicts transient poroelastic responses.

Achieves significant computational speed-up.

Handles heterogeneous permeability fields and variable timestamps.

Abstract

Machine learning-based data-driven modeling can allow computationally efficient time-dependent solutions of PDEs, such as those that describe subsurface multiphysical problems. In this work, our previous approach of conditional generative adversarial networks (cGAN) developed for the solution of steady-state problems involving highly heterogeneous material properties is extended to time-dependent problems by adopting the concept of continuous cGAN (CcGAN). The CcGAN that can condition continuous variables is developed to incorporate the time domain through either element-wise addition or conditional batch normalization. We note that this approach can accommodate other continuous variables (e.g., Young's modulus) similar to the time domain, which makes this framework highly flexible and extendable. Moreover, this framework can handle training data that contain different timestamps and then predict timestamps that do not exist in the training data. As a numerical example, 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.