Latent diffusion models for parameterization and data assimilation of facies-based geomodels

TL;DR

The paper addresses the challenge of high-dimensional, non-Gaussian geological parameterization for history matching in subsurface flow. It introduces latent diffusion models that couple a variational autoencoder for dimension reduction with a U-net denoiser to generate 2D multifacies geomodels in a reduced latent space, enabling fast and deterministic sampling via DDIM. Validation against object-based references shows that LDM realizations reproduce spatial statistics and flow responses with high fidelity, while enabling smooth parameter perturbations for data assimilation. When integrated with ensemble-based history matching (ESMDA) across cases with fixed and uncertain facies properties, the approach yields significant uncertainty reduction and posterior geomodels that bracket observed data. Overall, the work demonstrates that LDMs offer a practical, scalable framework for geomodel parameterization and data assimilation, with clear paths to 3D extension and alternative inference methods.

Abstract

Geological parameterization entails the representation of a geomodel using a small set of latent variables and a mapping from these variables to grid-block properties such as porosity and permeability. Parameterization is useful for data assimilation (history matching), as it maintains geological realism while reducing the number of variables to be determined. Diffusion models are a new class of generative deep-learning procedures that have been shown to outperform previous methods, such as generative adversarial networks, for image generation tasks. Diffusion models are trained to "denoise", which enables them to generate new geological realizations from input fields characterized by random noise. Latent diffusion models, which are the specific variant considered in this study, provide dimension reduction through use of a low-dimensional latent variable. The model developed in this work includes a variational autoencoder for dimension reduction and a U-net for the denoising process. Our application involves conditional 2D three-facies (channel-levee-mud) systems. The latent diffusion model is shown to provide realizations that are visually consistent with samples from geomodeling software. Quantitative metrics involving spatial and flow-response statistics are evaluated, and general agreement between the diffusion-generated models and reference realizations is observed. Stability tests are performed to assess the smoothness of the parameterization method. The latent diffusion model is then used for ensemble-based data assimilation. Two synthetic "true" models are considered. Significant uncertainty reduction, posterior P$_{10}$-P$_{90}$ forecasts that generally bracket observed data, and consistent posterior geomodels, are achieved in both cases.

Figures (16)

• Figure 1: Illustration of the diffusion process for a 2D channelized geomodel.
• Figure 2: Schematic representation of encoder-decoder and full LDM architecture (inspired by rombach2022highresolution).
• Figure 3: Architecture of the LDM used in this work. The values on the blocks/layers indicate the number of channels and dimensions.
• Figure 4: Training samples for three-facies models. The five conditioning points are shown in red. Colorbar in this figure applies to all subsequent figures of this type.
• Figure 5: Randomly selected Petrel and LDM-generated realizations of the three-facies system. Conditioning points shown in red.