Generation of non-stationary stochastic fields using Generative Adversarial Networks

TL;DR

The work tackles generating non-stationary geological facies conditioned on spatial maps $M$ using a concurrent-GAN framework with SPADE-based conditioning, enabling multiple realizations $G(z|M)$ without post-hoc optimization or extra losses. The method demonstrates strong conditioning, generalizes to unseen spatial modes in both 2D and 3D, and is validated on artificial and real datasets with flow simulations showing statistical fidelity to training samples. This approach offers a scalable, data-driven alternative to traditional MPS methods for conditioned geostatistical simulation, with potential impact on uncertainty quantification and reservoir management.

Abstract

In the context of generating geological facies conditioned on observed data, samples corresponding to all possible conditions are not generally available in the training set and hence the generation of these realizations depends primary on the generalization capability of the trained generative model. The problem becomes more complex when applied on non-stationary fields. In this work, we investigate the problem of using Generative Adversarial Networks (GANs) models to generate non-stationary geological channelized patterns and examine the models generalization capability at new spatial modes that were never seen in the given training set. The developed training method based on spatial-conditioning allowed for effective learning of the correlation between the spatial conditions (i.e. non-stationary maps) and the realizations implicitly without using additional loss terms or solving optimization problems for every new given data after training. In addition, our models can be trained on 2D and 3D samples. The results on real and artificial datasets show that we were able to generate geologically-plausible realizations beyond the training samples and with a strong correlation with the target maps.

Figures (19)

• Figure 1: Generator architecture: the stochastic input $z$ is projected into a generated image and the conditioning map is passed to each layer in the generator for spatial modulation. SPADE layer is similar to the one explained in park2019semantic.
• Figure 2: Discriminator architecture: the conditioning map is passed to convolutional layers and the resulting features are concatenated with the input image features (i.e., blue and green features). The discriminator output is the conditional probability of $x$ being real given its corresponding map $\textbf{M}$.
• Figure 3: Samples from the 2D datasets used to train GANs models. All images used to train the 2D models are of size $64\times 64$.
• Figure 4: Generated non-stationary realizations on the artificial dataset: the input conditioning maps are in the leftmost columns, the middle columns are the generated samples and the per-pixel mean maps are in the rightmost columns. The last four rows shows generated samples with never seen maps.
• Figure 5: Generated non-stationary realizations on the real masks of the Brahmaputra river: the input conditioning maps are in the leftmost columns, the middle columns are the generated samples and the per-pixel mean maps are in the rightmost columns. The last three rows shows generated samples with never seen maps