[Paper Review] Latent diffusion models for parameterization and data assimilation of facies-based geomodels

Guido Di Federico, Louis J. Durlofsky|ArXiv.org|Jun 21, 2024

Geological Modeling and Analysis4 citations

TL;DR

This paper proposes a latent diffusion model (LDM) for geological parameterization and data assimilation in 2D three-facies (channel-levee-mud) geomodels. By combining a variational autoencoder for dimensionality reduction and a U-Net for denoising, the LDM generates geologically realistic realizations and enables efficient history matching via ensemble-based methods, significantly reducing uncertainty while preserving key geological features.

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. PLEASE CITE AS: 10.1016/j.cageo.2024.105755 https://www.sciencedirect.com/science/article/pii/S0098300424002383 NOT WITH THE ARXIV VERSION

Motivation & Objective

• To develop a data-efficient, geologically realistic parameterization method for facies-based geomodels using deep generative models.
• To address the computational burden of history matching in large-scale subsurface flow models by reducing parameter dimensionality.
• To improve upon existing parameterization techniques—such as PCA, VAEs, and GANs—by leveraging the stability and sample quality of diffusion models.
• To enable robust data assimilation using the latent space of the diffusion model, ensuring posterior realizations match observed production data.
• To demonstrate the method’s effectiveness on synthetic 2D three-facies systems with both fixed and uncertain facies properties.

Proposed method

• The method employs a variational autoencoder (VAE) to map high-dimensional geomodels to a low-dimensional latent space, enabling efficient representation.
• A U-Net architecture is trained to perform the reverse denoising process, generating new realizations from random noise in the latent space.
• Conditional generation is achieved by incorporating hard data constraints during VAE training via a hard data loss term.
• The model is trained on 4,000 conditional realizations generated using Petrel, ensuring geological realism and data consistency.
• Ensemble-based data assimilation (ESMDA) is applied in the latent space to update the model using dynamic production data.
• Sampling uses DDIM (Denoising Diffusion Implicit Models) for fast, deterministic inference, enhancing computational efficiency.

Experimental results

Research questions

• RQ1 Can latent diffusion models generate geologically realistic 2D three-facies geomodels that match reference realizations in spatial and flow statistics?
• RQ2 How well does the LDM parameterization preserve geological features under data assimilation, especially with limited conditioning data?
• RQ3 Does the latent space enable stable, smooth transitions when latent variables are perturbed, indicating robustness?
• RQ4 To what extent can the LDM reduce uncertainty in porosity and permeability forecasts during history matching?
• RQ5 Can the method handle both fixed and uncertain facies property values in a unified framework?

Key findings

• The LDM-generated realizations exhibit strong visual and statistical consistency with reference models from Petrel, particularly in facies distribution and spatial continuity.
• Quantitative metrics, including spatial and flow-response statistics, show general agreement between LDM-generated and reference realizations.
• Stability tests confirm smooth parameterization, with minor perturbations in latent variables producing gradual, geologically plausible changes in output models.
• In both synthetic cases, data assimilation using ESMDA in the latent space reduced uncertainty, with posterior P10–P90 forecasts bracketing observed production data.
• For most facies, posterior distributions shifted toward the true values, with only log-permeability in mud showing limited sensitivity due to lack of well data.
• The mode of the posterior for mud permeability was 27 md, close to the true value of 40 md, indicating reasonable posterior concentration despite data insensitivity.