Parametrization of stochastic inputs using generative adversarial networks with application in geology
This addresses the challenge of high-dimensional, spatially correlated underground property modeling in geology, offering an incremental improvement over traditional parametric methods.
The paper tackled the problem of parametrizing stochastic inputs for numerical simulations by using generative adversarial networks (GANs) to emulate data distributions, applied to subsurface flow problems with binary channelized permeability. Results showed the method preserved visual realism and high-order statistics of flow responses while achieving a dimensionality reduction of two orders of magnitude.
We investigate artificial neural networks as a parametrization tool for stochastic inputs in numerical simulations. We address parametrization from the point of view of emulating the data generating process, instead of explicitly constructing a parametric form to preserve predefined statistics of the data. This is done by training a neural network to generate samples from the data distribution using a recent deep learning technique called generative adversarial networks. By emulating the data generating process, the relevant statistics of the data are replicated. The method is assessed in subsurface flow problems, where effective parametrization of underground properties such as permeability is important due to the high dimensionality and presence of high spatial correlations. We experiment with realizations of binary channelized subsurface permeability and perform uncertainty quantification and parameter estimation. Results show that the parametrization using generative adversarial networks is very effective in preserving visual realism as well as high order statistics of the flow responses, while achieving a dimensionality reduction of two orders of magnitude.