Adaptive regularisation for ensemble Kalman inversion

Iglesias, Marco A; Yang, Yuchen

Abstract

We propose a new regularisation strategy for the classical ensemble Kalman inversion (EKI) framework. The strategy consists of: (i) an adaptive choice for the regularisation parameter in the update formula in EKI, and (ii) criteria for the early stopping of the scheme. In contrast to existing approaches, our parameter choice does not rely on additional tuning parameters which often have severe effects on the efficiency of EKI. We motivate our approach using the interpretation of EKI as a Gaussian approximation in the Bayesian tempering setting for inverse problems. We show that our parameter choice controls the symmetrised Kullback–Leibler divergence between consecutive tempering measures. We further motivate our choice using a heuristic statistical discrepancy principle. We test our framework using electrical impedance tomography with the complete electrode model. Parameterisations of the unknown conductivity are employed which enable us to characterise both smooth or a discontinuous (piecewise-constant) fields. We show numerically that the proposed regularisation of EKI can produce efficient, robust and accurate estimates, even for the discontinuous case which tends to require larger ensembles and more iterations to converge. We compare the proposed technique with a standard method of choice and demonstrate that the proposed method is a viable choice to address computational efficiency of EKI in practical/operational settings.

Citation

Iglesias, M. A., & Yang, Y. (2021). Adaptive regularisation for ensemble Kalman inversion. Inverse Problems, 37(2), Article 025008. https://doi.org/10.1088/1361-6420/abd29b

• Journal Article Type: Article
• Acceptance Date: Dec 3, 2020
• Online Publication Date: Dec 10, 2020
• Publication Date: Feb 1, 2021
• Deposit Date: Dec 4, 2020
• Publicly Available Date: Dec 11, 2021
• Journal: Inverse Problems
• Print ISSN: 0266-5611
• Electronic ISSN: 1361-6420
• Publisher: IOP Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 37
• Issue: 2
• Article Number: 025008
• DOI: https://doi.org/10.1088/1361-6420/abd29b
• Keywords: Signal Processing; Theoretical Computer Science; Mathematical Physics; Applied Mathematics; Computer Science Applications
• Public URL: https://nottingham-repository.worktribe.com/output/5100606
• Publisher URL: http://iopscience.iop.org/0266-5611