Bayesian multiscale deep generative model for the solution of high-dimensional inverse problems

• URL: http://arxiv.org/abs/2102.03169v1
• Date: Thu, 4 Feb 2021 11:47:21 GMT
• Title: Bayesian multiscale deep generative model for the solution of high-dimensional inverse problems
• Authors: Yingzhi Xia, Nicholas Zabaras
• Abstract summary: 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Estimation of spatially-varying parameters for computationally expensive forward models governed by partial differential equations is addressed. A novel multiscale Bayesian inference approach is introduced based on deep probabilistic generative models. Such generative models provide a flexible representation by inferring on each scale a low-dimensional latent encoding while allowing hierarchical parameter generation from coarse- to fine-scales. Combining the multiscale generative model with Markov Chain Monte Carlo (MCMC), inference across scales is achieved enabling us to efficiently obtain posterior parameter samples at various scales. The estimation of coarse-scale parameters using a low-dimensional latent embedding captures global and notable parameter features using an inexpensive but inaccurate solver. MCMC sampling of the fine-scale parameters is enabled by utilizing the posterior information in the immediate coarser-scale. In this way, the global features are identified in the coarse-scale with inference of low-dimensional variables and inexpensive forward computation, and the local features are refined and corrected in the fine-scale. The developed method is demonstrated with two types of permeability estimation for flow in heterogeneous media. One is a Gaussian random field (GRF) with uncertain length scales, and the other is channelized permeability with the two regions defined by different GRFs. The obtained results indicate that the method allows high-dimensional parameter estimation while exhibiting stability, efficiency and accuracy.

Related papers

• Variational Bayesian surrogate modelling with application to robust design optimisation [0.9626666671366836]
  Surrogate models provide a quick-to-evaluate approximation to complex computational models. We consider Bayesian inference for constructing statistical surrogates with input uncertainties and dimensionality reduction. We demonstrate intrinsic and robust structural optimisation problems where cost functions depend on a weighted sum of the mean and standard deviation of model outputs.
  arXiv  Detail & Related papers  (2024-04-23T09:22:35Z)
• Data-freeWeight Compress and Denoise for Large Language Models [101.53420111286952]
  We propose a novel approach termed Data-free Joint Rank-k Approximation for compressing the parameter matrices. We achieve a model pruning of 80% parameters while retaining 93.43% of the original performance without any calibration data.
  arXiv  Detail & Related papers  (2024-02-26T05:51:47Z)
• Variational autoencoder with weighted samples for high-dimensional non-parametric adaptive importance sampling [0.0]
  We extend the existing framework to the case of weighted samples by introducing a new objective function. In order to add flexibility to the model and to be able to learn multimodal distributions, we consider a learnable prior distribution. We exploit the proposed procedure in existing adaptive importance sampling algorithms to draw points from a target distribution and to estimate a rare event probability in high dimension.
  arXiv  Detail & Related papers  (2023-10-13T15:40:55Z)
• Subsurface Characterization using Ensemble-based Approaches with Deep Generative Models [2.184775414778289]
  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.
  arXiv  Detail & Related papers  (2023-10-02T01:27:10Z)
• Heterogeneous Multi-Task Gaussian Cox Processes [61.67344039414193]
  We present a novel extension of multi-task Gaussian Cox processes for modeling heterogeneous correlated tasks jointly. A MOGP prior over the parameters of the dedicated likelihoods for classification, regression and point process tasks can facilitate sharing of information between heterogeneous tasks. We derive a mean-field approximation to realize closed-form iterative updates for estimating model parameters.
  arXiv  Detail & Related papers  (2023-08-29T15:01:01Z)
• Robust scalable initialization for Bayesian variational inference with multi-modal Laplace approximations [0.0]
  Variational mixtures with full-covariance structures suffer from a quadratic growth due to variational parameters with the number of parameters. We propose a method for constructing an initial Gaussian model approximation that can be used to warm-start variational inference.
  arXiv  Detail & Related papers  (2023-07-12T19:30:04Z)
• An iterative multi-fidelity approach for model order reduction of multi-dimensional input parametric PDE systems [0.0]
  We propose a sampling parametric strategy for the reduction of large-scale PDE systems with multidimensional input parametric spaces. It is achieved by exploiting low-fidelity models throughout the parametric space to sample points using an efficient sampling strategy. Since the proposed methodology leverages the use of low-fidelity models to assimilate the solution database, it significantly reduces the computational cost in the offline stage.
  arXiv  Detail & Related papers  (2023-01-23T15:25:58Z)
• Optimization of Annealed Importance Sampling Hyperparameters [77.34726150561087]
  Annealed Importance Sampling (AIS) is a popular algorithm used to estimates the intractable marginal likelihood of deep generative models. We present a parameteric AIS process with flexible intermediary distributions and optimize the bridging distributions to use fewer number of steps for sampling. We assess the performance of our optimized AIS for marginal likelihood estimation of deep generative models and compare it to other estimators.
  arXiv  Detail & Related papers  (2022-09-27T07:58:25Z)
• Counting Phases and Faces Using Bayesian Thermodynamic Integration [77.34726150561087]
  We introduce a new approach to reconstruction of the thermodynamic functions and phase boundaries in two-parametric statistical mechanics systems. We use the proposed approach to accurately reconstruct the partition functions and phase diagrams of the Ising model and the exactly solvable non-equilibrium TASEP.
  arXiv  Detail & Related papers  (2022-05-18T17:11:23Z)
• A Model for Multi-View Residual Covariances based on Perspective Deformation [88.21738020902411]
  We derive a model for the covariance of the visual residuals in multi-view SfM, odometry and SLAM setups. We validate our model with synthetic and real data and integrate it into photometric and feature-based Bundle Adjustment.
  arXiv  Detail & Related papers  (2022-02-01T21:21:56Z)
• Inverting brain grey matter models with likelihood-free inference: a tool for trustable cytoarchitecture measurements [62.997667081978825]
  characterisation of the brain grey matter cytoarchitecture with quantitative sensitivity to soma density and volume remains an unsolved challenge in dMRI. We propose a new forward model, specifically a new system of equations, requiring a few relatively sparse b-shells. We then apply modern tools from Bayesian analysis known as likelihood-free inference (LFI) to invert our proposed model.
  arXiv  Detail & Related papers  (2021-11-15T09:08:27Z)

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.