Generating large 3D images can be useful in many applications from geoscience to medical imagery to battery modelling etc... Here we focus on a geoscience application where the 3D images correspond to possible realizations of some subsurface properties such as the permeability or the rock type.
Our objective is to use GAN for dimensional reduction to solve an inverse problem. In fact the subsurface model is very uncertain: we have some geostatistical tools that can generate different possible images but we need to find those who are in accordance with surface data (some observations wells).
The application of this method could range from oil & gas to hydrogeology to CO2 geological storage. The challenge we want to focus here is to build a GAN method that scale well with image size in terms of GPU memory and in terms of training time. Another essential feature of the solution is that the latent space should be kept reasonably small (<100) as this will be used in a subsequent inverse problem solution.
Existing solutions can be found in the literature to address this problem. A basic solution is the patch-based approach consisting in splitting the image in different patches and training them separately [1,2]. The problem with this approach is that it can miss large geological structures coherency that are very important to keep in geoscience applications. A more interesting approach discussed in [3] present a method based on subsequent training of images at different resolutions.
More precisely the initial image is first downscaled and trained with a GAN and subsequently they generate different patches of successively growing resolutions that are conditioned to the coarser image. The approach is used for medical images, but it uses also object edges as a condition that are not available in our application. The code for this approach is publicly available and could be used as a starting point for the study.
The case study is a geoscience application, the training dataset is publicly available at
Zenodo and it is composed by 1000 3D images of size 512X512X16.
A 2D illustration of the geological images is shown in figure below. The data was generated by a computer program (Process based channelized reservoir models). The objective is to train a GAN for this set of images using multi-gpu or quantum computing. Different papers have addressed this problem, but using generally 2D images or smaller images [4].
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- Lei, Y., Wang, T., Liu, Y., Higgins, K., Tian, S., Liu, T., Mao, H., Shim, H., Curran, W.J., Shu, H.K., Yang, X.: MRI-based synthetic CT generation using deep convolutional neural network. In: SPIE Medical Imaging. vol. 10949 (2019)
- Uzunova, H., Ehrhardt, J., Jacob, F., Frydrychowicz, A., Handels, H. (2019). Multi-scale GANs for Memory-efficient Generation of High Resolution Medical Images. In: , et
al. Medical Image Computing and Computer Assisted Intervention – MICCAI 2019. MICCAI 2019. Lecture Notes in Computer Science(), vol 11769. Springer, Cham. paper Code available at: code
- Sun, C. and Demyanov, V. and Arnold, D. : Comparison of popular Generative Adversarial Network flavours for fluvial reservoir modelling 2021 European Association of Geoscientists & Engineers, paper
- Sun, C., Demyanov, V. & Arnold, D. Geological realism in Fluvial facies modelling with GAN under variable depositional conditions. Comput Geosci (2023).
