Matches in SemOpenAlex for { <https://semopenalex.org/work/W4315705714> ?p ?o ?g. }
Showing items 1 to 61 of
61
with 100 items per page.
- W4315705714 abstract "Obtaining lightweight and accurate approximations of Hessian applies in inverse problems governed by partial differential equations (PDEs) is an essential task to make both deterministic and Bayesian statistical large-scale inverse problems computationally tractable. The $mathcal{O}(N^{3})$ computational complexity of dense linear algebraic routines such as that needed for sampling from Gaussian proposal distributions and Newton solves by direct linear methods, can be reduced to log-linear complexity by utilizing hierarchical off-diagonal low-rank (HODLR) matrix approximations. In this work, we show that a class of Hessians that arise from inverse problems governed by PDEs are well approximated by the HODLR matrix format. In particular, we study inverse problems governed by PDEs that model the instantaneous viscous flow of ice sheets. In these problems, we seek a spatially distributed basal sliding parameter field such that the flow predicted by the ice sheet model is consistent with ice sheet surface velocity observations. We demonstrate the use of HODLR approximation by efficiently generating Hessian approximations that allow fast generation of samples from a Gaussianized posterior proposal distribution. Computational studies are performed which illustrate ice sheet problem regimes for which the Gauss-Newton data-misfit Hessian is more efficiently approximated by the HODLR matrix format than the low-rank (LR) format. We then demonstrate that HODLR approximations can be favorable, when compared to global low-rank approximations, for large-scale problems by studying the data-misfit Hessian associated to inverse problems governed by the Stokes flow model on the Humboldt glacier and Greenland ice sheets." @default.
- W4315705714 created "2023-01-12" @default.
- W4315705714 creator A5005111063 @default.
- W4315705714 creator A5012373865 @default.
- W4315705714 creator A5028037951 @default.
- W4315705714 creator A5057284080 @default.
- W4315705714 creator A5076542592 @default.
- W4315705714 date "2023-01-09" @default.
- W4315705714 modified "2023-09-25" @default.
- W4315705714 title "Hierarchical off-diagonal low-rank approximation of Hessians in inverse problems, with application to ice sheet model initializaiton" @default.
- W4315705714 doi "https://doi.org/10.48550/arxiv.2301.03644" @default.
- W4315705714 hasPublicationYear "2023" @default.
- W4315705714 type Work @default.
- W4315705714 citedByCount "0" @default.
- W4315705714 crossrefType "posted-content" @default.
- W4315705714 hasAuthorship W4315705714A5005111063 @default.
- W4315705714 hasAuthorship W4315705714A5012373865 @default.
- W4315705714 hasAuthorship W4315705714A5028037951 @default.
- W4315705714 hasAuthorship W4315705714A5057284080 @default.
- W4315705714 hasAuthorship W4315705714A5076542592 @default.
- W4315705714 hasBestOaLocation W43157057141 @default.
- W4315705714 hasConcept C106487976 @default.
- W4315705714 hasConcept C114614502 @default.
- W4315705714 hasConcept C134306372 @default.
- W4315705714 hasConcept C135252773 @default.
- W4315705714 hasConcept C159985019 @default.
- W4315705714 hasConcept C164226766 @default.
- W4315705714 hasConcept C192562407 @default.
- W4315705714 hasConcept C203616005 @default.
- W4315705714 hasConcept C207467116 @default.
- W4315705714 hasConcept C2524010 @default.
- W4315705714 hasConcept C28826006 @default.
- W4315705714 hasConcept C33923547 @default.
- W4315705714 hasConceptScore W4315705714C106487976 @default.
- W4315705714 hasConceptScore W4315705714C114614502 @default.
- W4315705714 hasConceptScore W4315705714C134306372 @default.
- W4315705714 hasConceptScore W4315705714C135252773 @default.
- W4315705714 hasConceptScore W4315705714C159985019 @default.
- W4315705714 hasConceptScore W4315705714C164226766 @default.
- W4315705714 hasConceptScore W4315705714C192562407 @default.
- W4315705714 hasConceptScore W4315705714C203616005 @default.
- W4315705714 hasConceptScore W4315705714C207467116 @default.
- W4315705714 hasConceptScore W4315705714C2524010 @default.
- W4315705714 hasConceptScore W4315705714C28826006 @default.
- W4315705714 hasConceptScore W4315705714C33923547 @default.
- W4315705714 hasLocation W43157057141 @default.
- W4315705714 hasOpenAccess W4315705714 @default.
- W4315705714 hasPrimaryLocation W43157057141 @default.
- W4315705714 hasRelatedWork W1569479001 @default.
- W4315705714 hasRelatedWork W1724331128 @default.
- W4315705714 hasRelatedWork W1972453316 @default.
- W4315705714 hasRelatedWork W1976219569 @default.
- W4315705714 hasRelatedWork W1991295960 @default.
- W4315705714 hasRelatedWork W2010068234 @default.
- W4315705714 hasRelatedWork W2113940432 @default.
- W4315705714 hasRelatedWork W2322946133 @default.
- W4315705714 hasRelatedWork W2755893905 @default.
- W4315705714 hasRelatedWork W2964005990 @default.
- W4315705714 isParatext "false" @default.
- W4315705714 isRetracted "false" @default.
- W4315705714 workType "article" @default.