Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Probabilistic learning inference of boundary value problem with
  uncertainties based on Kullback-Leibler divergence under implicit constraints   In a first part, we present a mathematical analysis of a general methodology
of a probabilistic learning inference that allows for estimating a posterior
probability model for a stochastic boundary value problem from a prior
probability model. The given targets are statistical moments for which the
underlying realizations are not available. Under these conditions, the
Kullback-Leibler divergence minimum principle is used for estimating the
posterior probability measure. A statistical surrogate model of the implicit
mapping, which represents the constraints, is introduced. The MCMC generator
and the necessary numerical elements are given to facilitate the implementation
of the methodology in a parallel computing framework. In a second part, an
application is presented to illustrate the proposed theory and is also, as
such, a contribution to the three-dimensional stochastic homogenization of
heterogeneous linear elastic media in the case of a non-separation of the
microscale and macroscale. For the construction of the posterior probability
measure by using the probabilistic learning inference, in addition to the
constraints defined by given statistical moments of the random effective
elasticity tensor, the second-order moment of the random normalized residue of
the stochastic partial differential equation has been added as a constraint.
This constraint guarantees that the algorithm seeks to bring the statistical
moments closer to their targets while preserving a small residue.

27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an