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

arXiv: https://arxiv.org/abs/2111.14984 · HTML: https://mlsanity.com/paper/2111.14984/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Nov 2021.

## Built on by (most cited first, 9 of 9)

- [gLaSDI: Parametric Physics-informed Greedy Latent Space Dynamics Identification](https://mlsanity.com/paper/2204.12005/) (2022)
- [Physics-informed active learning with simultaneous weak-form latent space dynamics identification](https://mlsanity.com/paper/2407.00337/) (2024)
- [Machine learning for modelling unstructured grid data in computational physics: a review](https://mlsanity.com/paper/2502.09346/) (2025)
- [CCDM: Continuous Conditional Diffusion Models for Image Generation](https://mlsanity.com/paper/2405.03546/) (2024)
- [Generative Adversarial Reduced Order Modelling](https://mlsanity.com/paper/2305.15881/) (2023)
- [Turning Waste into Wealth: Leveraging Low-Quality Samples for Enhancing Continuous Conditional Generative Adversarial Networks](https://mlsanity.com/paper/2308.10273/) (2023)
- [A generalized machine learning framework for brittle crack problems using transfer learning and graph neural networks](https://mlsanity.com/paper/2211.12459/) (2022)
- [Deep operator network for surrogate modeling of poroelasticity with random permeability fields](https://mlsanity.com/paper/2509.11966/) (2025)
- [Subsurface Characterization using Ensemble-based Approaches with Deep Generative Models](https://mlsanity.com/paper/2310.00839/) (2023)

## Abstract (arXiv)

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.