Iterated Kalman methodology for inverse problems
نویسندگان
چکیده
This paper is focused on the optimization approach to solution of inverse problems. We introduce a stochastic dynamical system in which parameter-to-data map embedded, with goal employing techniques from nonlinear Kalman filtering estimate parameter given data. The extended filter (which we refer as ExKI context problems) can be effective for some problems approached this way, but impractical when forward not readily differentiable and black box, also high dimensional spaces because need propagate large covariance matrices. Application ensemble filters, example use inversion (EKI) algorithm, has emerged useful tool overcomes both these issues: it derivative free works low-rank approximation formed ensemble. In paper, work ExKI, EKI, variant EKI term unscented (UKI). contains two main contributions. Firstly, identify novel embedded. present theory linear case show exponential convergence mean distribution regularized least squares problem. contrast previous been employed where used leads algebraic an unregularized Secondly, that application UKI yields improved results, comparison same system. numerical experiments include proof-of-concept examples various applied problems: learning permeability parameters subsurface flow; damage field structure deformation; Navier-Stokes initial condition data at positive times; subgrid-scale general circulation model (GCM) time-averaged statistics. • A filtering-based method systems. Derive extended, ensemble, inversions induces form Tikhonov regularization overcome ill-posedness. Prove features Test 8 problems, including calibrating 3D climate model.
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ژورنال
عنوان ژورنال: Journal of Computational Physics
سال: 2022
ISSN: ['1090-2716', '0021-9991']
DOI: https://doi.org/10.1016/j.jcp.2022.111262