Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hyper-Differential Sensitivity Analysis for Inverse Problems Constrained
  by Partial Differential Equations   High fidelity models used in many science and engineering applications couple
multiple physical states and parameters. Inverse problems arise when a model
parameter cannot be determined directly, but rather is estimated using
(typically sparse and noisy) measurements of the states. The data is usually
not sufficient to simultaneously inform all of the parameters. Consequently,
the governing model typically contains parameters which are uncertain but must
be specified for a complete model characterization necessary to invert for the
parameters of interest. We refer to the combination of the additional model
parameters (those which are not inverted for) and the measured data states as
the "complementary parameters". We seek to quantify the relative importance of
these complementary parameters to the solution of the inverse problem. To
address this, we present a framework based on hyper-differential sensitivity
analysis (HDSA). HDSA computes the derivative of the solution of an inverse
problem with respect to complementary parameters. We present a mathematical
framework for HDSA in large-scale PDE-constrained inverse problems and show how
HDSA can be interpreted to give insight about the inverse problem. We
demonstrate the effectiveness of the method on an inverse problem by estimating
a permeability field, using pressure and concentration measurements, in a
porous medium flow application with uncertainty in the boundary conditions,
source injection, and diffusion coefficient.

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The categories of this paper are: nucl-th
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The categories of this paper are: stat
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The categories of this paper are: astro-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: econ
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The categories of this paper are: q-bio
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The categories of this paper are: supr-con
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: physics
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The categories of this paper are: plasm-ph
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The categories of this paper are: math-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th