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MaxEnt approach for the probabilistic modeling of matrix-valued random fields with constrained eigenvalues: application to apparent mechanical and transport properties

Johann Guilleminot 1 Christian Soize 1
1 Mechanics
MSME - Laboratoire de Modélisation et Simulation Multi Echelle
Abstract : This work is devoted to the construction of a class of prior stochastic models for non-Gaussian positive-definite matrix-valued random fields, having recourse to the maximum entropy (MaxEnt) principle. Specifically, the proposed approach aims at taking into account, in addition to usual constraints (e.g. normalization condition for the p.d.f., invertibility, etc.), some information related to the variances of some selected eigenvalues. After having recalled the general stochastic framework, we will present some mathematical derivations and discuss a few fundamental properties of the proposed class. It will be shown that the latter is basically parameterized by a set of spatial correlation lengths, a real-valued deterministic field controlling the overall level of statistical fluctuations and a Rm -valued deterministic field controlling the variances of m selected random eigenvalues. Computational issues, related in particular to random generation, will be discussed.
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https://hal-upec-upem.archives-ouvertes.fr/hal-00701530
Contributor : Christian Soize <>
Submitted on : Friday, May 25, 2012 - 3:35:21 PM
Last modification on : Thursday, March 19, 2020 - 11:52:05 AM

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  • HAL Id : hal-00701530, version 1

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Johann Guilleminot, Christian Soize. MaxEnt approach for the probabilistic modeling of matrix-valued random fields with constrained eigenvalues: application to apparent mechanical and transport properties. 6th MIT Conference on Computational Fluid and Solid Mechanics, Advances in Solids and Structures, Jun 2011, Cambridge, Massachusetts, United States. pp.1. ⟨hal-00701530⟩

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