Neural Network Projections for Local-to-Global Permeability Mapping

Abstract Neural networks have become increasingly popular in STEM in recent years, mainly due to their potential to provide fast surrogate models for standard PDE solvers and offer flexible parametrization options. This is particularly valuable for MCMC-based inverse In this presentation, we adopt a local perspective: using convolutional neural networks to replace conventional KLE projection matrices that map local log-permeability samples to the global field. This approach not only provides another opportunity for stochastic dimension reduction but, more importantly, introduces additional flexibility. The neural network projection can be trained to relate local samples with varying correlation lengths. We also investigate the integration of VAE models for representing local fields.problems, where the solver must be called repeatedly. In this context, techniques based on domain decomposition are widely used. In geophysics, Variational Autoencoders (VAE) have been successfully applied to generate permeability fields in porous media. Similar to the Karhunen-Loève expansion, VAEs can reduce the stochastic dimensionality of the problem while offering greater generality.

Slides

Photos

Participants: 10