Fractal Informed Generative Adversarial Networks (FI-GAN): Application to the generation of X-ray CT images of a self-similar partially saturated sand

The recent increase in data availability fostered the development of new and more powerful data-driven numerical models, particularly machine learning. With a limited quantity of data in geomechanics applications, machine learning often suffers from unstable training and lack of convergence. Physics informed machine learning models have been proposed in the literature to mitigate the issue as an alternative to data-only approaches. In the present work, a new machine learning method is proposed: Fractal Informed Generative Adversarial Networks (FI-GAN) and applied to a case of X-ray CT images of partially saturated sand. This method consists of training an informed adversarial model using pore fractal dimension. The semi-supervision provided by pore fractal metrics presents two advantages, firstly, it regularises the training; secondly, improves the distribution of pore fractal dimension, which is correlated with permeability. Results show that the generated images improve the fractal distribution of the informer phase in the partially saturated material (i.e., water) and the other two phases. The approach is validated with physics flow simulations. The generated images can be applied in the calibration of image processing tools, filling missing data in X-ray CT scans, generating microscales in multiscale applications, and data augmentation, among others.