FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W1901718912> ?p ?o ?g. }

• W1901718912 endingPage "1921" @default.
• W1901718912 startingPage "1906" @default.
• W1901718912 abstract "Variational methods are widely used to solve geophysical inverse problems. Although gradient‐based minimization algorithms are available for high‐dimensional problems (dimension >10 6 ), they do not provide an estimate of the errors in the optimal solution. In this study, we assess the performance of several numerical methods to approximate the analysis‐error covariance matrix, assuming reasonably linear models. The evaluation is performed for a CO 2 flux estimation problem using synthetic remote‐sensing observations of CO 2 columns. A low‐dimensional experiment is considered in order to compare the analysis error approximations to a full‐rank finite‐difference inverse Hessian estimate, followed by a realistic high‐dimensional application. Two stochastic approaches, a Monte‐Carlo simulation and a method based on random gradients of the cost function, produced analysis error variances with a relative error <10 % . The long‐distance error correlations due to sampling noise are significantly less pronounced for the gradient‐based randomization, which is also particularly attractive when implemented in parallel. Deterministic evaluations of the inverse Hessian using the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm are also tested. While existing BFGS preconditioning techniques yield poor approximations of the error variances (relative error >120 % ), a new preconditioner that efficiently accumulates information on the diagonal of the inverse Hessian dramatically improves the results (relative error <50 % ). Furthermore, performing several cycles of the BFGS algorithm using the same gradient and vector pairs enhances its performance (relative error <30 % ) and is necessary to obtain convergence. Leveraging those findings, we proposed a BFGS hybrid approach which combines the new preconditioner with several BFGS cycles using information from a few (3–5) Monte‐Carlo simulations. Its performance is comparable to the stochastic approximations for the low‐dimensional case, while good scalability is obtained for the high‐dimensional experiment. Potential applications of these new BFGS methods range from characterizing the information content of high‐dimensional inverse problems to improving the convergence rate of current minimization algorithms." @default.
• W1901718912 created "2016-06-24" @default.
• W1901718912 creator A5021569445 @default.
• W1901718912 creator A5025366851 @default.
• W1901718912 creator A5032751311 @default.
• W1901718912 creator A5051079243 @default.
• W1901718912 creator A5052745301 @default.
• W1901718912 creator A5055794878 @default.
• W1901718912 creator A5058462310 @default.
• W1901718912 creator A5082056142 @default.
• W1901718912 date "2015-01-07" @default.
• W1901718912 modified "2023-10-16" @default.
• W1901718912 title "Improved analysis‐error covariance matrix for high‐dimensional variational inversions: application to source estimation using a 3D atmospheric transport model" @default.
• W1901718912 cites W1512208174 @default.
• W1901718912 cites W1534488808 @default.
• W1901718912 cites W1567803238 @default.
• W1901718912 cites W1965446559 @default.
• W1901718912 cites W1969247870 @default.
• W1901718912 cites W1971047944 @default.
• W1901718912 cites W1974959374 @default.
• W1901718912 cites W1976748077 @default.
• W1901718912 cites W1989575957 @default.
• W1901718912 cites W1991867732 @default.
• W1901718912 cites W1995518538 @default.
• W1901718912 cites W2010394974 @default.
• W1901718912 cites W2017014514 @default.
• W1901718912 cites W2029062149 @default.
• W1901718912 cites W2030356704 @default.
• W1901718912 cites W2042803051 @default.
• W1901718912 cites W2048163104 @default.
• W1901718912 cites W2051669046 @default.
• W1901718912 cites W2059808679 @default.
• W1901718912 cites W2062294426 @default.
• W1901718912 cites W2066455064 @default.
• W1901718912 cites W2079598576 @default.
• W1901718912 cites W2103459312 @default.
• W1901718912 cites W2117876399 @default.
• W1901718912 cites W2123923268 @default.
• W1901718912 cites W2127093080 @default.
• W1901718912 cites W2128217321 @default.
• W1901718912 cites W2129841493 @default.
• W1901718912 cites W2130520941 @default.
• W1901718912 cites W2130844535 @default.
• W1901718912 cites W2139004160 @default.
• W1901718912 cites W2145411928 @default.
• W1901718912 cites W2170838091 @default.
• W1901718912 cites W2173190456 @default.
• W1901718912 cites W2179584279 @default.
• W1901718912 cites W4245985820 @default.
• W1901718912 doi "https://doi.org/10.1002/qj.2495" @default.
• W1901718912 hasPublicationYear "2015" @default.
• W1901718912 type Work @default.
• W1901718912 sameAs 1901718912 @default.
• W1901718912 citedByCount "49" @default.
• W1901718912 countsByYear W19017189122014 @default.
• W1901718912 countsByYear W19017189122015 @default.
• W1901718912 countsByYear W19017189122016 @default.
• W1901718912 countsByYear W19017189122017 @default.
• W1901718912 countsByYear W19017189122018 @default.
• W1901718912 countsByYear W19017189122019 @default.
• W1901718912 countsByYear W19017189122020 @default.
• W1901718912 countsByYear W19017189122021 @default.
• W1901718912 countsByYear W19017189122022 @default.
• W1901718912 countsByYear W19017189122023 @default.
• W1901718912 crossrefType "journal-article" @default.
• W1901718912 hasAuthorship W1901718912A5021569445 @default.
• W1901718912 hasAuthorship W1901718912A5025366851 @default.
• W1901718912 hasAuthorship W1901718912A5032751311 @default.
• W1901718912 hasAuthorship W1901718912A5051079243 @default.
• W1901718912 hasAuthorship W1901718912A5052745301 @default.
• W1901718912 hasAuthorship W1901718912A5055794878 @default.
• W1901718912 hasAuthorship W1901718912A5058462310 @default.
• W1901718912 hasAuthorship W1901718912A5082056142 @default.
• W1901718912 hasConcept C105795698 @default.
• W1901718912 hasConcept C11413529 @default.
• W1901718912 hasConcept C122383733 @default.
• W1901718912 hasConcept C126255220 @default.
• W1901718912 hasConcept C132721684 @default.
• W1901718912 hasConcept C151319957 @default.
• W1901718912 hasConcept C178650346 @default.
• W1901718912 hasConcept C185142706 @default.
• W1901718912 hasConcept C203616005 @default.
• W1901718912 hasConcept C207467116 @default.
• W1901718912 hasConcept C2524010 @default.
• W1901718912 hasConcept C28826006 @default.
• W1901718912 hasConcept C31258907 @default.
• W1901718912 hasConcept C33923547 @default.
• W1901718912 hasConcept C41008148 @default.
• W1901718912 hasConceptScore W1901718912C105795698 @default.
• W1901718912 hasConceptScore W1901718912C11413529 @default.
• W1901718912 hasConceptScore W1901718912C122383733 @default.
• W1901718912 hasConceptScore W1901718912C126255220 @default.
• W1901718912 hasConceptScore W1901718912C132721684 @default.
• W1901718912 hasConceptScore W1901718912C151319957 @default.
• W1901718912 hasConceptScore W1901718912C178650346 @default.
• W1901718912 hasConceptScore W1901718912C185142706 @default.
• W1901718912 hasConceptScore W1901718912C203616005 @default.
• W1901718912 hasConceptScore W1901718912C207467116 @default.

• next