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

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.

References in corpus (10)

• Conditional Generative Adversarial Nets
• Modulating early visual processing by language
• Deep generative models in inversion: a review and development of a new approach based on a variational autoencoder
• Non-intrusive reduced order modeling of natural convection in porous media using convolutional autoencoders: comparison with linear subspace techniques
• Component-wise reduced order model lattice-type structure design
• Reduced order models for Lagrangian hydrodynamics
• Accelerating design optimization using reduced order models
• A Locally Conservative Mixed Finite Element Framework for Coupled Hydro-Mechanical-Chemical Processes in Heterogeneous Porous Media
• Non-intrusive reduced order modeling of poroelasticity of heterogeneous media based on a discontinuous Galerkin approximation
• Enriched Galerkin Discretization for Modeling Poroelasticity and Permeability Alteration in Heterogeneous Porous Media

Cited by in corpus (1)

• Physics-informed active learning with simultaneous weak-form latent space dynamics identification