mlsanityData to 7 Oct 2026

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

arXiv 2102.03169 ↗First posted 4 Feb 2021stat.ML cs.LGcited by 12

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Abstract (arXiv)

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.

Key facts. Cited by 12 papers in the map (data through 7 Oct 2026). Builds on 31 of its 75 references that are in the map. First posted on arXiv 4 Feb 2021.

Builds on

31 of 75 references.

References · 31

  1. 2015Deep Residual Learning for Image Recognitioncited by 51,809
  2. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  3. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  4. 2013Auto-Encoding Variational Bayescited by 3,980
  5. 2013Visualizing and Understanding Convolutional Networkscited by 2,278
  6. 2015Variational Inference with Normalizing Flowscited by 2,161
  7. 2016Variational Inference: A Review for Statisticianscited by 1,466
  8. 2014NICE: Non-linear Independent Components Estimationcited by 1,052
  9. 2016InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Netscited by 858
  10. 2018Residual Dense Network for Image Super-Resolutioncited by 796
  11. 2018Towards a Definition of Disentangled Representationscited by 294
  12. 2018Bayesian Deep Convolutional Encoder-Decoder Networks for Surrogate Modeling and Uncertainty Quantificationcited by 199
19 more
  1. 2018Survey of multifidelity methods in uncertainty propagation, inference, and optimizationcited by 141
  2. 2018Robustly Disentangled Causal Mechanisms: Validating Deep Representations for Interventional Robustnesscited by 108
  3. 2019A deep-learning-based surrogate model for data assimilation in dynamic subsurface flow problemscited by 59
  4. 2018Deep convolutional encoder-decoder networks for uncertainty quantification of dynamic multiphase flow in heterogeneous mediacited by 56
  5. 2018Stochastic seismic waveform inversion using generative adversarial networks as a geological priorcited by 47
  6. 2020Solving inverse problems using conditional invertible neural networkscited by 37
  7. 2018Structured Uncertainty Prediction Networkscited by 34
  8. 2017Training-image based geostatistical inversion using a spatial generative adversarial neural networkcited by 31
  9. 2018Deep autoregressive neural networks for high-dimensional inverse problems in groundwater contaminant source identificationcited by 26
  10. 2017Inversion using a new low-dimensional representation of complex binary geological media based on a deep neural networkcited by 24
  11. 2018Towards a Robust Parameterization for Conditioning Facies Models Using Deep Variational Autoencoders and Ensemble Smoothercited by 16
  12. 2020Multi-Resolution A*cited by 13
  13. 2018Structured Bayesian Gaussian process latent variable model: applications to data-driven dimensionality reduction and high-dimensional inversioncited by 9
  14. 2018A Deep-Learning-Based Geological Parameterization for History Matching Complex Modelscited by 7
  15. 2019Integration of adversarial autoencoders with residual dense convolutional networks for estimation of non-Gaussian hydraulic conductivitiescited by 7
  16. 2018Predictive Collective Variable Discovery with Deep Bayesian Modelscited by 5
  17. 2018Beyond black-boxes in Bayesian inverse problems and model validation: applications in solid mechanics of elastographycited by 3
  18. 2019Multilevel Dimension-Independent Likelihood-Informed MCMC for Large-Scale Inverse Problemscited by 3
  19. 2019ANOVA Gaussian process modeling for high-dimensional stochastic computational modelscited by 2

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 0; 2023: 3; 2024: 3; 2025: 2; 2026: 3.

12 papers.

  1. 2023A domain-decomposed VAE method for Bayesian inverse problemscited by 6
  2. 2024Deep adaptive sampling for surrogate modeling without labeled datacited by 5
  3. 2024Bayesian neural networks for predicting uncertainty in full-field material responsecited by 5
  4. 2023VI-DGP: A variational inference method with deep generative prior for solving high-dimensional inverse problemscited by 4
  5. 2021Deep Learning for Simultaneous Inference of Hydraulic and Transport Propertiescited by 3
  6. 2026Noise-Adaptive Diffusion Sampling for Inverse Problems Without Task-Specific Tuningcited by 2
  7. 2023Dimension-reduced KRnet maps for high-dimensional Bayesian inverse problemscited by 1
  8. 2024The Deep Latent Space Particle Filter for Real-Time Data Assimilation with Uncertainty Quantificationcited by 1
  9. 2025Bayesian Inverse Problems Meet Flow Matching: Efficient and Flexible Inference via Transformerscited by 0
  10. 2025Variational Autoencoder for Generating Broader-Spectrum prior Proposals in Markov chain Monte Carlo Methodscited by 0
  11. 2026GenPANIS: A Latent-Variable Generative Framework for Forward and Inverse PDE Problems in Multiphase Mediacited by 0
  12. 2026Deep Adaptive Dimension Reduction for Bayesian Inference in Inverse Problemscited by 0