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

• URL: http://arxiv.org/abs/2406.14815v4
• Date: Mon, 14 Oct 2024 18:14:56 GMT
• Title: Latent diffusion models for parameterization and data assimilation of facies-based geomodels
• Authors: Guido Di Federico, Louis J. Durlofsky,
• Abstract summary: Diffusion models are trained to generate new geological realizations from input fields characterized by random noise. Latent diffusion models are shown to provide realizations that are visually consistent with samples from geomodeling software.
• Score: 0.0
• License:
• 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.

Related papers

• Distillation of Discrete Diffusion through Dimensional Correlations [21.078500510691747]
  "Mixture" models in discrete diffusion are capable of treating dimensional correlations while remaining scalable. We empirically demonstrate that our proposed method for discrete diffusions work in practice, by distilling a continuous-time discrete diffusion model pretrained on the CIFAR-10 dataset.
  arXiv  Detail & Related papers  (2024-10-11T10:53:03Z)
• Diffusion-HMC: Parameter Inference with Diffusion Model driven Hamiltonian Monte Carlo [2.048226951354646]
  This work uses a single diffusion generative model to address the interlinked objectives of generating predictions for observed astrophysical fields from theory and constraining physical models from observations using these predictions. We leverage the approximate likelihood of the diffusion generative model to derive tight constraints on cosmology by using the Hamiltonian Monte Carlo method to sample the posterior on cosmological parameters for a given test image.
  arXiv  Detail & Related papers  (2024-05-08T17:59:03Z)
• Synthetic location trajectory generation using categorical diffusion models [50.809683239937584]
  Diffusion models (DPMs) have rapidly evolved to be one of the predominant generative models for the simulation of synthetic data. We propose using DPMs for the generation of synthetic individual location trajectories (ILTs) which are sequences of variables representing physical locations visited by individuals.
  arXiv  Detail & Related papers  (2024-02-19T15:57:39Z)
• Towards Theoretical Understandings of Self-Consuming Generative Models [56.84592466204185]
  This paper tackles the emerging challenge of training generative models within a self-consuming loop. We construct a theoretical framework to rigorously evaluate how this training procedure impacts the data distributions learned by future models. We present results for kernel density estimation, delivering nuanced insights such as the impact of mixed data training on error propagation.
  arXiv  Detail & Related papers  (2024-02-19T02:08:09Z)
• Learning Generative Models for Lumped Rainfall-Runoff Modeling [3.69758875412828]
  This study presents a novel generative modeling approach to rainfall-runoff modeling, focusing on the synthesis of realistic daily catchment runoff time series. Unlike traditional process-based lumped hydrologic models, our approach uses a small number of latent variables to characterize runoff generation processes. In this study, we trained the generative models using neural networks on data from over 3,000 global catchments and achieved prediction accuracies comparable to current deep learning models.
  arXiv  Detail & Related papers  (2023-09-18T16:07:41Z)
• Geometric Neural Diffusion Processes [55.891428654434634]
  We extend the framework of diffusion models to incorporate a series of geometric priors in infinite-dimension modelling. We show that with these conditions, the generative functional model admits the same symmetry.
  arXiv  Detail & Related papers  (2023-07-11T16:51:38Z)
• A Geometric Perspective on Diffusion Models [57.27857591493788]
  We inspect the ODE-based sampling of a popular variance-exploding SDE. We establish a theoretical relationship between the optimal ODE-based sampling and the classic mean-shift (mode-seeking) algorithm.
  arXiv  Detail & Related papers  (2023-05-31T15:33:16Z)
• Score Approximation, Estimation and Distribution Recovery of Diffusion Models on Low-Dimensional Data [68.62134204367668]
  This paper studies score approximation, estimation, and distribution recovery of diffusion models, when data are supported on an unknown low-dimensional linear subspace. We show that with a properly chosen neural network architecture, the score function can be both accurately approximated and efficiently estimated. The generated distribution based on the estimated score function captures the data geometric structures and converges to a close vicinity of the data distribution.
  arXiv  Detail & Related papers  (2023-02-14T17:02:35Z)
• Score-based Continuous-time Discrete Diffusion Models [102.65769839899315]
  We extend diffusion models to discrete variables by introducing a Markov jump process where the reverse process denoises via a continuous-time Markov chain. We show that an unbiased estimator can be obtained via simple matching the conditional marginal distributions. We demonstrate the effectiveness of the proposed method on a set of synthetic and real-world music and image benchmarks.
  arXiv  Detail & Related papers  (2022-11-30T05:33:29Z)
• Diffusion Causal Models for Counterfactual Estimation [18.438307666925425]
  We consider the task of counterfactual estimation from observational imaging data given a known causal structure. We propose Diff-SCM, a deep structural causal model that builds on recent advances of generative energy-based models. We find that Diff-SCM produces more realistic and minimal counterfactuals than baselines on MNIST data and can also be applied to ImageNet data.
  arXiv  Detail & Related papers  (2022-02-21T12:23:01Z)
• Variational Mixture of Normalizing Flows [0.0]
  Deep generative models, such as generative adversarial networks autociteGAN, variational autoencoders autocitevaepaper, and their variants, have seen wide adoption for the task of modelling complex data distributions. Normalizing flows have overcome this limitation by leveraging the change-of-suchs formula for probability density functions. The present work overcomes this by using normalizing flows as components in a mixture model and devising an end-to-end training procedure for such a model.
  arXiv  Detail & Related papers  (2020-09-01T17:20:08Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.