Imperial College London
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Professor Grigorios A. Pavliotis

Faculty of Natural Sciences, Department of Mathematics

Professor of Applied Mathematics
 
 
 
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Contact

 

+44 (0)20 7594 8564g.pavliotis Website

 
 
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Location

 

736aHuxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Pavliotis:2022:10.1137/21m1397416,
author = {Pavliotis, GA and Stuart, AM and Vaes, U},
doi = {10.1137/21m1397416},
journal = {SIAM Journal on Applied Dynamical Systems},
pages = {284--326},
title = {Derivative-free Bayesian inversion using multiscale dynamics},
url = {http://dx.doi.org/10.1137/21m1397416},
volume = {21},
year = {2022}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - Inverse problems are ubiquitous because they formalize the integration of data with mathematical models. In many scientific applications the forward model is expensive to evaluate, and adjoint computations are difficult to employ; in this setting derivative-free methods which involve a small number of forward model evaluations are an attractive proposition. Ensemble Kalman-based interacting particle systems (and variants such as consensus-based and unscented Kalman approaches) have proven empirically successful in this context, but suffer from the fact that they cannot be systematically refined to return the true solution, except in the setting of linear forward models [A. Garbuno-Inigo et al., SIAM J. Appl. Dyn. Syst., 19 (2020), pp. 412--441]. In this paper, we propose a new derivative-free approach to Bayesian inversion, which may be employed for posterior sampling or for maximum a posteriori estimation, and may be systematically refined. The method relies on a fast/slow system of stochastic differential equations for the local approximation of the gradient of the log-likelihood appearing in a Langevin diffusion. Furthermore the method may be preconditioned by use of information from ensemble Kalman--based methods (and variants), providing a methodology which leverages the documented advantages of those methods, while also being provably refinable. We define the methodology, highlighting its flexibility and many variants, provide a theoretical analysis of the proposed approach, and demonstrate its efficacy by means of numerical experiments.
AU  - Pavliotis,GA
AU  - Stuart,AM
AU  - Vaes,U
DO  - 10.1137/21m1397416
EP  - 326
PY  - 2022///
SN  - 1536-0040
SP  - 284
TI  - Derivative-free Bayesian inversion using multiscale dynamics
T2  - SIAM Journal on Applied Dynamical Systems
UR  - http://dx.doi.org/10.1137/21m1397416
UR  - https://epubs.siam.org/doi/10.1137/21M1397416
UR  - http://hdl.handle.net/10044/1/94448
VL  - 21
ER  -
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