Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized Rough Polyharmonic Splines for Multiscale PDEs with Rough
  Coefficients   In this paper, we demonstrate the construction of generalized Rough
Polyhamronic Splines (GRPS) within the Bayesian framework, in particular, for
multiscale PDEs with rough coefficients. The optimal coarse basis can be
derived automatically by the randomization of the original PDEs with a proper
prior distribution and the conditional expectation given partial information on
edge or derivative measurements. We prove the (quasi)-optimal localization and
approximation properties of the obtained bases, and justify the theoretical
results with numerical experiments.

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The categories of this paper are: eess
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-ex
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: econ
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The categories of this paper are: math-ph