Subsurface Characterization using Ensemble-based Approaches with Deep Generative Models

• URL: http://arxiv.org/abs/2310.00839v2
• Date: Tue, 10 Oct 2023 02:25:28 GMT
• Title: Subsurface Characterization using Ensemble-based Approaches with Deep Generative Models
• Authors: Jichao Bao, Hongkyu Yoon, and Jonghyun Lee
• Abstract summary: Inverse modeling is limited for ill-posed, high-dimensional applications due to computational costs and poor prediction accuracy with sparse datasets. We combine Wasserstein Geneversarative Adrial Network with Gradient Penalty (WGAN-GP) and Ensemble Smoother with Multiple Data Assimilation (ES-MDA) WGAN-GP is trained to generate high-dimensional K fields from a low-dimensional latent space and ES-MDA updates the latent variables by assimilating available measurements.
• Score: 2.184775414778289
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Estimating spatially distributed properties such as hydraulic conductivity (K) from available sparse measurements is a great challenge in subsurface characterization. However, the use of inverse modeling is limited for ill-posed, high-dimensional applications due to computational costs and poor prediction accuracy with sparse datasets. In this paper, we combine Wasserstein Generative Adversarial Network with Gradient Penalty (WGAN-GP), a deep generative model that can accurately capture complex subsurface structure, and Ensemble Smoother with Multiple Data Assimilation (ES-MDA), an ensemble-based inversion method, for accurate and accelerated subsurface characterization. WGAN-GP is trained to generate high-dimensional K fields from a low-dimensional latent space and ES-MDA then updates the latent variables by assimilating available measurements. Several subsurface examples are used to evaluate the accuracy and efficiency of the proposed method and the main features of the unknown K fields are characterized accurately with reliable uncertainty quantification. Furthermore, the estimation performance is compared with a widely-used variational, i.e., optimization-based, inversion approach, and the proposed approach outperforms the variational inversion method, especially for the channelized and fractured field examples. We explain such superior performance by visualizing the objective function in the latent space: because of nonlinear and aggressive dimension reduction via generative modeling, the objective function surface becomes extremely complex while the ensemble approximation can smooth out the multi-modal surface during the minimization. This suggests that the ensemble-based approach works well over the variational approach when combined with deep generative models at the cost of forward model runs unless convergence-ensuring modifications are implemented in the variational inversion.

Related papers

• Total Uncertainty Quantification in Inverse PDE Solutions Obtained with Reduced-Order Deep Learning Surrogate Models [50.90868087591973]
  We propose an approximate Bayesian method for quantifying the total uncertainty in inverse PDE solutions obtained with machine learning surrogate models. We test the proposed framework by comparing it with the iterative ensemble smoother and deep ensembling methods for a non-linear diffusion equation.
  arXiv  Detail & Related papers  (2024-08-20T19:06:02Z)
• Distributionally Robust Optimization as a Scalable Framework to Characterize Extreme Value Distributions [22.765095010254118]
  The goal of this paper is to develop distributionally robust optimization (DRO) estimators, specifically for multidimensional Extreme Value Theory (EVT) statistics. In order to mitigate over-conservative estimates while enhancing out-of-sample performance, we study DRO estimators informed by semi-parametric max-stable constraints in the space of point processes. Both approaches are validated using synthetically generated data, recovering prescribed characteristics, and verifying the efficacy of the proposed techniques.
  arXiv  Detail & Related papers  (2024-07-31T19:45:27Z)
• Probabilistic Reduced-Dimensional Vector Autoregressive Modeling with Oblique Projections [0.7614628596146602]
  We propose a reduced-dimensional vector autoregressive model to extract low-dimensional dynamics from noisy data. An optimal oblique decomposition is derived for the best predictability regarding prediction error covariance. The superior performance and efficiency of the proposed approach are demonstrated using data sets from a synthesized Lorenz system and an industrial process from Eastman Chemical.
  arXiv  Detail & Related papers  (2024-01-14T05:38:10Z)
• Generative Modeling with Phase Stochastic Bridges [49.4474628881673]
  Diffusion models (DMs) represent state-of-the-art generative models for continuous inputs. We introduce a novel generative modeling framework grounded in textbfphase space dynamics Our framework demonstrates the capability to generate realistic data points at an early stage of dynamics propagation.
  arXiv  Detail & Related papers  (2023-10-11T18:38:28Z)
• Dynamic Kernel-Based Adaptive Spatial Aggregation for Learned Image Compression [63.56922682378755]
  We focus on extending spatial aggregation capability and propose a dynamic kernel-based transform coding. The proposed adaptive aggregation generates kernel offsets to capture valid information in the content-conditioned range to help transform. Experimental results demonstrate that our method achieves superior rate-distortion performance on three benchmarks compared to the state-of-the-art learning-based methods.
  arXiv  Detail & Related papers  (2023-08-17T01:34:51Z)
• Conditional Korhunen-Lo\'{e}ve regression model with Basis Adaptation for high-dimensional problems: uncertainty quantification and inverse modeling [62.997667081978825]
  We propose a methodology for improving the accuracy of surrogate models of the observable response of physical systems. We apply the proposed methodology to constructing surrogate models via the Basis Adaptation (BA) method of the stationary hydraulic head response.
  arXiv  Detail & Related papers  (2023-07-05T18:14:38Z)
• VTAE: Variational Transformer Autoencoder with Manifolds Learning [144.0546653941249]
  Deep generative models have demonstrated successful applications in learning non-linear data distributions through a number of latent variables. The nonlinearity of the generator implies that the latent space shows an unsatisfactory projection of the data space, which results in poor representation learning. We show that geodesics and accurate computation can substantially improve the performance of deep generative models.
  arXiv  Detail & Related papers  (2023-04-03T13:13:19Z)
• Generalised Latent Assimilation in Heterogeneous Reduced Spaces with Machine Learning Surrogate Models [10.410970649045943]
  We develop a system which combines reduced-order surrogate models with a novel data assimilation technique. Generalised Latent Assimilation can benefit both the efficiency provided by the reduced-order modelling and the accuracy of data assimilation.
  arXiv  Detail & Related papers  (2022-04-07T15:13:12Z)
• Extension of Dynamic Mode Decomposition for dynamic systems with incomplete information based on t-model of optimal prediction [69.81996031777717]
  The Dynamic Mode Decomposition has proved to be a very efficient technique to study dynamic data. The application of this approach becomes problematic if the available data is incomplete because some dimensions of smaller scale either missing or unmeasured. We consider a first-order approximation of the Mori-Zwanzig decomposition, state the corresponding optimization problem and solve it with the gradient-based optimization method.
  arXiv  Detail & Related papers  (2022-02-23T11:23:59Z)
• Bayesian multiscale deep generative model for the solution of high-dimensional inverse problems [0.0]
  A novel multiscale Bayesian inference approach is introduced based on deep probabilistic generative models. The method allows high-dimensional parameter estimation while exhibiting stability, efficiency and accuracy.
  arXiv  Detail & Related papers  (2021-02-04T11:47:21Z)

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.