Generative Displacement Model

Abstract

Generative models are often based on statistical physics or game theory, such as Latent Diffusion Models (LDMs) or Generative Adversarial Networks (GANs). This study relies on two-phase displacement in porous media, where one fluid displaces another, to introduce a Generative Displacement Model (GDM). The introduced model uses weight functions derived from effective density and flow rate in the latent space. The weight functions are compared with the mixing rules of diffusion-based models, providing insight into generative behavior and performance. The proposed approach is evaluated using 5,508 shale fracture images and benchmarked against an LDM. A grid search was conducted using 200,000 training steps over learning rates from 1×10⁻⁵ to 5×10⁻⁵. The best-performing GDM achieved a Fréchet Inception Distance (FID) of 15.7, comparable to 16.6 for the LDM trained similarly, though hyperparameters beyond learning rate were not tuned. The generated images show realistic fracture patterns and surface textures of the original dataset. The results show that multiphase transport physics offers an interesting and less explored basis for generative model design.