Posterior sampling with CNN-based, Plug-and-Play regularization with applications to Post-Stack Seismic Inversion

• URL: http://arxiv.org/abs/2212.14595v1
• Date: Fri, 30 Dec 2022 08:20:49 GMT
• Title: Posterior sampling with CNN-based, Plug-and-Play regularization with applications to Post-Stack Seismic Inversion
• Authors: Muhammad Izzatullah, Tariq Alkhalifah, Juan Romero, Miguel Corrales, Nick Luiken, Matteo Ravasi
• Abstract summary: Uncertainty quantification is crucial to inverse problems, as it could provide valuable information about the inversion results. We present a framework that performs posterior inference by implicitly regularizing the Kullback-Leibler divergence loss with a CNN-based denoiser. We call this algorithm new Plug-and-Play Stein Vari-SVGD and demonstrate its ability in producing high-resolution, trustworthy samples.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Uncertainty quantification is crucial to inverse problems, as it could provide decision-makers with valuable information about the inversion results. For example, seismic inversion is a notoriously ill-posed inverse problem due to the band-limited and noisy nature of seismic data. It is therefore of paramount importance to quantify the uncertainties associated to the inversion process to ease the subsequent interpretation and decision making processes. Within this framework of reference, sampling from a target posterior provides a fundamental approach to quantifying the uncertainty in seismic inversion. However, selecting appropriate prior information in a probabilistic inversion is crucial, yet non-trivial, as it influences the ability of a sampling-based inference in providing geological realism in the posterior samples. To overcome such limitations, we present a regularized variational inference framework that performs posterior inference by implicitly regularizing the Kullback-Leibler divergence loss with a CNN-based denoiser by means of the Plug-and-Play methods. We call this new algorithm Plug-and-Play Stein Variational Gradient Descent (PnP-SVGD) and demonstrate its ability in producing high-resolution, trustworthy samples representative of the subsurface structures, which we argue could be used for post-inference tasks such as reservoir modelling and history matching. To validate the proposed method, numerical tests are performed on both synthetic and field post-stack seismic data.

Related papers

• Full-waveform earthquake source inversion using simulation-based inference [0.0]
  We present a novel framework for full-waveform seismic source inversion using simulation-based inference ( SBI) We show that SBI produces well-calibrated posteriors that generally agree with the true seismic source parameters. We apply our methodology to a pair of moderate magnitude earthquakes in the North Atlantic.
  arXiv  Detail & Related papers  (2024-10-30T17:25:57Z)
• Uncertainty Quantification in Seismic Inversion Through Integrated Importance Sampling and Ensemble Methods [2.2530496464901106]
  In deep learning-based seismic inversion, uncertainty arises from various sources, including data noise, neural network design and training, and inherent data limitations. This study introduces a novel approach to uncertainty quantification in seismic inversion by integrating ensemble methods with importance sampling.
  arXiv  Detail & Related papers  (2024-09-10T19:53:12Z)
• Stochastic full waveform inversion with deep generative prior for uncertainty quantification [0.0]
  Full Waveform Inversion (FWI) involves solving a nonlinear and often non-unique inverse problem. FWI presents challenges such as local minima trapping and inadequate handling of inherent uncertainties. We propose leveraging deep generative models as the prior distribution of geophysical parameters for Bayesian inversion.
  arXiv  Detail & Related papers  (2024-06-07T11:44:50Z)
• Towards stable real-world equation discovery with assessing differentiating quality influence [52.2980614912553]
  We propose alternatives to the commonly used finite differences-based method. We evaluate these methods in terms of applicability to problems, similar to the real ones, and their ability to ensure the convergence of equation discovery algorithms.
  arXiv  Detail & Related papers  (2023-11-09T23:32:06Z)
• Calibrating Neural Simulation-Based Inference with Differentiable Coverage Probability [50.44439018155837]
  We propose to include a calibration term directly into the training objective of the neural model. By introducing a relaxation of the classical formulation of calibration error we enable end-to-end backpropagation. It is directly applicable to existing computational pipelines allowing reliable black-box posterior inference.
  arXiv  Detail & Related papers  (2023-10-20T10:20:45Z)
• Reliable amortized variational inference with physics-based latent distribution correction [0.4588028371034407]
  A neural network is trained to approximate the posterior distribution over existing pairs of model and data. The accuracy of this approach relies on the availability of high-fidelity training data. We show that our correction step improves the robustness of amortized variational inference with respect to changes in number of source experiments, noise variance, and shifts in the prior distribution.
  arXiv  Detail & Related papers  (2022-07-24T02:38:54Z)
• Sampling-free Variational Inference for Neural Networks with Multiplicative Activation Noise [51.080620762639434]
  We propose a more efficient parameterization of the posterior approximation for sampling-free variational inference. Our approach yields competitive results for standard regression problems and scales well to large-scale image classification tasks.
  arXiv  Detail & Related papers  (2021-03-15T16:16:18Z)
• Leveraging Global Parameters for Flow-based Neural Posterior Estimation [90.21090932619695]
  Inferring the parameters of a model based on experimental observations is central to the scientific method. A particularly challenging setting is when the model is strongly indeterminate, i.e., when distinct sets of parameters yield identical observations. We present a method for cracking such indeterminacy by exploiting additional information conveyed by an auxiliary set of observations sharing global parameters.
  arXiv  Detail & Related papers  (2021-02-12T12:23:13Z)
• Uncertainty quantification in imaging and automatic horizon tracking: a Bayesian deep-prior based approach [0.5156484100374059]
  Uncertainty quantification (UQ) deals with a probabilistic description of the solution nonuniqueness and data noise sensitivity. In this paper, we focus on how UQ trickles down to horizon tracking for the determination of stratigraphic models.
  arXiv  Detail & Related papers  (2020-04-01T04:26:33Z)
• Spatially Adaptive Inference with Stochastic Feature Sampling and Interpolation [72.40827239394565]
  We propose to compute features only at sparsely sampled locations. We then densely reconstruct the feature map with an efficient procedure. The presented network is experimentally shown to save substantial computation while maintaining accuracy over a variety of computer vision tasks.
  arXiv  Detail & Related papers  (2020-03-19T15:36:31Z)
• Semiparametric Bayesian Forecasting of Spatial Earthquake Occurrences [77.68028443709338]
  We propose a fully Bayesian formulation of the Epidemic Type Aftershock Sequence (ETAS) model. The occurrence of the mainshock earthquakes in a geographical region is assumed to follow an inhomogeneous spatial point process.
  arXiv  Detail & Related papers  (2020-02-05T10:11:26Z)

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.