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Upscaling and downscaling Monte Carlo ensembles with generative models

Scheiter, Matthias; Valentine, Andrew; Sambridge, Malcolm

Upscaling and downscaling Monte Carlo ensembles with generative models Thumbnail


Matthias Scheiter

Malcolm Sambridge


Monte Carlo methods are widespread in geophysics and have proved to be powerful in non-linear inverse problems. However, they are associated with significant practical challenges, including long calculation times, large output ensembles of Earth models, and difficulties in the appraisal of the results. This paper addresses some of these challenges using generative models, a family of tools that have recently attracted much attention in the machine learning literature. Generative models can, in principle, learn a probability distribution from a set of given samples and also provide a means for rapid generation of new samples which follow that approximated distribution. These two features make them well suited for application to the outputs of Monte Carlo algorithms. In particular, training a generative model on the posterior distribution of a Bayesian inference problem provides two main possibilities. First, the number of parameters in the generative model is much smaller than the number of values stored in the ensemble, leading to large compression rates. Secondly, once trained, the generative model can be used to draw any number of samples, thereby eliminating the dependence on an often large and unwieldy ensemble. These advantages pave new pathways for the use of Monte Carlo ensembles, including improved storage and communication of the results, enhanced calculation of numerical integrals, and the potential for convergence assessment of the Monte Carlo procedure. Here, these concepts are initially demonstrated using a simple synthetic example that scales into higher dimensions. They are then applied to a large ensemble of shear wave velocity models of the core–mantle boundary, recently produced in a Monte Carlo study. These examples demonstrate the effectiveness of using generative models to approximate posterior ensembles, and indicate directions to address various challenges in Monte Carlo inversion.

Journal Article Type Article
Acceptance Date Mar 8, 2022
Online Publication Date Mar 10, 2022
Publication Date 2022-08
Deposit Date Apr 19, 2022
Publicly Available Date Apr 19, 2022
Journal Geophysical Journal International
Print ISSN 0956-540X
Electronic ISSN 1365-246X
Publisher Oxford University Press
Peer Reviewed Peer Reviewed
Volume 230
Issue 2
Pages 916-931
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Copyright Statement
© The Author(s) 2022. Published by Oxford University Press on behalf of The Royal Astronomical Society.
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (, which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.

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