Deep Learning-Based Multiresolution Parameterization for Spatially Adaptive Model Updating

TL;DR: In this article , a new deep learning-based parameterization approach for model calibration with spatial adaptivity and multiresolution representation is presented, which can facilitate the integration of data at different resolutions while enabling updates to the desired regions of the domain.

Abstract:  This paper presents a new deep learning-based parameterization approach for model calibration with two important properties: spatial adaptivity and multiresolution representation. The method aims to establish a spatially adaptive multiresolution latent space representation of subsurface property maps that enables local updates to property distributions at different scales. The deep learning model consists of a convolutional neural network architecture that learns successive mapping across multiple scales, from a coarse grid to increasingly finer grid representations. Once trained, the architecture learns latent spaces that encode spatial information across multiple scales. The resulting parameterization can facilitate the integration of data at different resolutions while enabling updates to the desired regions of the domain. Unlike the standard deep learning latent variables that are not localized and do not provide spatial adaptivity, the presented method enables local update capability that can be exploited to incorporate expert knowledge into assisted model updating workflows. Examples with two-dimensional multi-Gaussian random fields are used to introduce the method and its properties, followed by application of the method to a travel-time tomography inverse problem to investigate its model updating performance.