Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Data-Scalable Randomized Misfit Approach for Solving Large-Scale
  PDE-Constrained Inverse Problems   A randomized misfit approach is presented for the efficient solution of
large-scale PDE-constrained inverse problems with high-dimensional data. The
purpose of this paper is to offer a theory-based framework for random
projections in this inverse problem setting. The stochastic approximation to
the misfit is analyzed using random projection theory. By expanding beyond mean
estimator convergence, a practical characterization of randomized misfit
convergence can be achieved. The theoretical results developed hold with any
valid random projection in the literature. The class of feasible distributions
is broad yet simple to characterize compared to previous stochastic misfit
methods. This class includes very sparse random projections which provide
additional computational benefit. A different proof for a variant of the
Johnson-Lindenstrauss lemma is also provided. This leads to a different
intuition for the $O(\epsilon^{-2})$ factor in bounds for Johnson-Lindenstrauss
results. The main contribution of this paper is a theoretical result showing
the method guarantees a valid solution for small reduced misfit dimensions. The
interplay between Johnson-Lindenstrauss theory and Morozov's discrepancy
principle is shown to be essential to the result. The computational cost
savings for large-scale PDE-constrained problems with high- dimensional data is
discussed. Numerical verification of the developed theory is presented for
model problems of estimating a distributed parameter in an elliptic partial
differential equation. Results with different random projections are presented
to demonstrate the viability and accuracy of the proposed approach.

20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
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The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph