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International Journal for Uncertainty Quantification

Publicou 6 edições por ano

ISSN Imprimir: 2152-5080

ISSN On-line: 2152-5099

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HYPERDIFFERENTIAL SENSITIVITY ANALYSIS OF UNCERTAIN PARAMETERS IN PDE-CONSTRAINED OPTIMIZATION

Volume 10, Edição 3, 2020, pp. 225-248
DOI: 10.1615/Int.J.UncertaintyQuantification.2020032480
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RESUMO

Many problems in engineering and sciences require the solution of large scale optimization constrained by partial differential equations (PDEs). Though PDE-constrained optimization is itself challenging, most applications pose additional complexity, namely, uncertain parameters in the PDEs. Uncertainty quantification (UQ) is necessary to characterize, prioritize, and study the influence of these uncertain parameters. Sensitivity analysis, a classical tool in UQ, is frequently used to study the sensitivity of a model to uncertain parameters. In this article, we introduce "hyperdifferential sensitivity analysis" which considers the sensitivity of the solution of a PDE-constrained optimization problem to uncertain parameters. Our approach is a goal-oriented analysis which may be viewed as a tool to complement other UQ methods in the service of decision making and robust design. We formally define hyperdifferential sensitivity indices and highlight their relationship to the existing optimization and sensitivity analysis literatures. Assuming the presence of low rank structure in the parameter space, computational efficiency is achieved by leveraging a generalized singular value decomposition in conjunction with a randomized solver which converts the computational bottleneck of the algorithm into an embarrassingly parallel loop. Two multiphysics examples, consisting of nonlinear steady state control and transient linear inversion, demonstrate efficient identification of the uncertain parameters which have the greatest influence on the optimal solution.

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CITADO POR
  1. Saibaba Arvind K., Hart Joseph, Bloemen Waanders Bart, Randomized algorithms for generalized singular value decomposition with application to sensitivity analysis, Numerical Linear Algebra with Applications, 28, 4, 2021. Crossref

  2. Sunseri Isaac, Hart Joseph, van Bloemen Waanders Bart, Alexanderian Alen, Hyper-differential sensitivity analysis for inverse problems constrained by partial differential equations, Inverse Problems, 36, 12, 2020. Crossref

  3. Stevens Mason, Sunseri Isaac, Alexanderian Alen, Hyper-differential sensitivity analysis for inverse problems governed by ODEs with application to COVID-19 modeling, Mathematical Biosciences, 351, 2022. Crossref

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