Enhanced uncertainty quantification variational autoencoders for the solution of Bayesian inverse problems

• URL: http://arxiv.org/abs/2502.13105v1
• Date: Tue, 18 Feb 2025 18:17:49 GMT
• Title: Enhanced uncertainty quantification variational autoencoders for the solution of Bayesian inverse problems
• Authors: Andrea Tonini, Luca Dede',
• Abstract summary: We build upon existing research by proposing a novel loss function to train variational autoencoders for inverse problems. We provide a theoretical proof of the convergence of the latent states of variational autoencoders to the posterior distribution of the model parameters.
• Score: 0.0
• License:
• Abstract: Among other uses, neural networks are a powerful tool for solving deterministic and Bayesian inverse problems in real-time. In the Bayesian framework, variational autoencoders, a specialized type of neural network, enable the estimation of model parameters and their distribution based on observational data allowing to perform real-time inverse uncertainty quantification. In this work, we build upon existing research [Goh, H. et al., Proceedings of Machine Learning Research, 2022] by proposing a novel loss function to train variational autoencoders for Bayesian inverse problems. When the forward map is affine, we provide a theoretical proof of the convergence of the latent states of variational autoencoders to the posterior distribution of the model parameters. We validate this theoretical result through numerical tests and we compare the proposed variational autoencoder with the existing one in the literature. Finally, we test the proposed variational autoencoder on the Laplace equation.

Related papers

• Deep Operator Networks for Bayesian Parameter Estimation in PDEs [0.0]
  We present a novel framework combining Deep Operator Networks (DeepONets) with Physics-Informed Neural Networks (PINNs) to solve partial differential equations (PDEs) By integrating data-driven learning with physical constraints, our method achieves robust and accurate solutions across diverse scenarios.
  arXiv  Detail & Related papers  (2025-01-18T07:41:05Z)
• 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)
• A probabilistic, data-driven closure model for RANS simulations with aleatoric, model uncertainty [1.8416014644193066]
  We propose a data-driven, closure model for Reynolds-averaged Navier-Stokes (RANS) simulations that incorporates aleatoric, model uncertainty. A fully Bayesian formulation is proposed, combined with a sparsity-inducing prior in order to identify regions in the problem domain where the parametric closure is insufficient.
  arXiv  Detail & Related papers  (2023-07-05T16:53:31Z)
• Posterior Collapse and Latent Variable Non-identifiability [54.842098835445]
  We propose a class of latent-identifiable variational autoencoders, deep generative models which enforce identifiability without sacrificing flexibility. Across synthetic and real datasets, latent-identifiable variational autoencoders outperform existing methods in mitigating posterior collapse and providing meaningful representations of the data.
  arXiv  Detail & Related papers  (2023-01-02T06:16:56Z)
• Variational Laplace Autoencoders [53.08170674326728]
  Variational autoencoders employ an amortized inference model to approximate the posterior of latent variables. We present a novel approach that addresses the limited posterior expressiveness of fully-factorized Gaussian assumption. We also present a general framework named Variational Laplace Autoencoders (VLAEs) for training deep generative models.
  arXiv  Detail & Related papers  (2022-11-30T18:59:27Z)
• A Variational Inference Approach to Inverse Problems with Gamma Hyperpriors [60.489902135153415]
  This paper introduces a variational iterative alternating scheme for hierarchical inverse problems with gamma hyperpriors. The proposed variational inference approach yields accurate reconstruction, provides meaningful uncertainty quantification, and is easy to implement.
  arXiv  Detail & Related papers  (2021-11-26T06:33:29Z)
• Training on Test Data with Bayesian Adaptation for Covariate Shift [96.3250517412545]
  Deep neural networks often make inaccurate predictions with unreliable uncertainty estimates. We derive a Bayesian model that provides for a well-defined relationship between unlabeled inputs under distributional shift and model parameters. We show that our method improves both accuracy and uncertainty estimation.
  arXiv  Detail & Related papers  (2021-09-27T01:09:08Z)
• Autoencoding Variational Autoencoder [56.05008520271406]
  We study the implications of this behaviour on the learned representations and also the consequences of fixing it by introducing a notion of self consistency. We show that encoders trained with our self-consistency approach lead to representations that are robust (insensitive) to perturbations in the input introduced by adversarial attacks.
  arXiv  Detail & Related papers  (2020-12-07T14:16:14Z)
• Bayesian neural networks and dimensionality reduction [4.039245878626346]
  A class of model-based approaches for such problems includes latent variables in an unknown non-linear regression function. VAEs are artificial neural networks (ANNs) that employ approximations to make computation tractable. We deploy Markov chain Monte Carlo sampling algorithms for Bayesian inference in ANN models with latent variables.
  arXiv  Detail & Related papers  (2020-08-18T17:11:07Z)
• Unlabelled Data Improves Bayesian Uncertainty Calibration under Covariate Shift [100.52588638477862]
  We develop an approximate Bayesian inference scheme based on posterior regularisation. We demonstrate the utility of our method in the context of transferring prognostic models of prostate cancer across globally diverse populations.
  arXiv  Detail & Related papers  (2020-06-26T13:50:19Z)

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.