Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Solving Inverse Problems for Steady-State Equations using A Multiple
  Criteria Model with Collage Distance, Entropy, and Sparsity   In this paper, we extend the previous method for solving inverse problems for
steady-state equations using the Generalized Collage Theorem by searching for
an approximation that not only minimizes the collage error but also maximizes
the entropy and minimize the sparsity. In this extended formulation, the
parameter estimation minimization problem can be understood as a multiple
criteria problem, with three different and conflicting criteria: The
generalized collage error, the entropy associated with the unknown parameters,
and the sparsity of the set of unknown parameters. We implement a scalarization
technique to reduce the multiple criteria program to a single criterion one, by
combining all objective functions with different trade-off weights. Numerical
examples confirm that the collage method produces good, but sub-optimal,
results. A relatively low-weighted entropy term allows for better
approximations while the sparsity term decreases the complexity of the solution
in terms of the number of elements in the basis.

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The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
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The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
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The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
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The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th