English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

We consider optimal design of PDE-based Bayesian linear inverse problems withinfinite-dimensional parameters. We focus on the A-optimal design criterion,defined as the average posterior variance and quantified by the trace of theposterior covariance operator. We propose using structure exploiting randomizedmethods to compute the A-optimal objective function and its gradient, andprovide a detailed analysis of the error for the proposed estimators. To ensuresparse and binary design vectors, we develop a novel reweighted$\ell_1$-minimization algorithm. We also introduce a modified A-optimalcriterion and present randomized estimators for its efficient computation. Wepresent numerical results illustrating the proposed methods on a modelcontaminant source identification problem, where the inverse problem seeks torecover the initial state of a contaminant plume, using discrete measurementsof the contaminant in space and time.

Randomization and reweighted $\ell_1$-minimization for A-optimal design of linear inverse problems