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Bibliographic Details
Main Authors: Borges, Marcio, Pereira, Felipe, Tosin, Michel
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2507.00020
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author Borges, Marcio
Pereira, Felipe
Tosin, Michel
author_facet Borges, Marcio
Pereira, Felipe
Tosin, Michel
contents This study uses a Variational Autoencoder method to enhance the efficiency and applicability of Markov Chain Monte Carlo (McMC) methods by generating broader-spectrum prior proposals. Traditional approaches, such as the Karhunen-Loève Expansion (KLE), require previous knowledge of the covariance function, often unavailable in practical applications. The VAE framework enables a data-driven approach to flexibly capture a broader range of correlation structures in Bayesian inverse problems, particularly subsurface flow modeling. The methodology is tested on a synthetic groundwater flow inversion problem, where pressure data is used to estimate permeability fields. Numerical experiments demonstrate that the VAE-based parameterization achieves comparable accuracy to KLE when the correlation length is known and outperforms KLE when the assumed correlation length deviates from the true value. Moreover, the VAE approach significantly reduces stochastic dimensionality, improving computational efficiency. The results suggest that leveraging deep generative models in McMC methods can lead to more adaptable and efficient Bayesian inference in high-dimensional problems.
format Preprint
id arxiv_https___arxiv_org_abs_2507_00020
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Variational Autoencoder for Generating Broader-Spectrum prior Proposals in Markov chain Monte Carlo Methods
Borges, Marcio
Pereira, Felipe
Tosin, Michel
Machine Learning
This study uses a Variational Autoencoder method to enhance the efficiency and applicability of Markov Chain Monte Carlo (McMC) methods by generating broader-spectrum prior proposals. Traditional approaches, such as the Karhunen-Loève Expansion (KLE), require previous knowledge of the covariance function, often unavailable in practical applications. The VAE framework enables a data-driven approach to flexibly capture a broader range of correlation structures in Bayesian inverse problems, particularly subsurface flow modeling. The methodology is tested on a synthetic groundwater flow inversion problem, where pressure data is used to estimate permeability fields. Numerical experiments demonstrate that the VAE-based parameterization achieves comparable accuracy to KLE when the correlation length is known and outperforms KLE when the assumed correlation length deviates from the true value. Moreover, the VAE approach significantly reduces stochastic dimensionality, improving computational efficiency. The results suggest that leveraging deep generative models in McMC methods can lead to more adaptable and efficient Bayesian inference in high-dimensional problems.
title Variational Autoencoder for Generating Broader-Spectrum prior Proposals in Markov chain Monte Carlo Methods
topic Machine Learning
url https://arxiv.org/abs/2507.00020