Volume 55, Number 2, March-April 2021
|Page(s)||355 - 393|
|Published online||23 March 2021|
Maximum Entropy on the Mean approach to solve generalized inverse problems with an application in computational thermodynamics
Institut de Mathématiques de Toulouse, Toulouse, France
2 ANITI Toulouse.
3 ISAS – Service de la Corrosion et du Comportement des Matériaux dans leur Environnement (SCCME), CEA, Université Paris-Saclay, F-91191 Gif-sur-Yvette, France
4 Ecole Nationale d’Aviation Civile, Toulouse, France
Accepted: 14 January 2021
In this paper, we study entropy maximisation problems in order to reconstruct functions or measures subject to very general integral constraints. Our work has a twofold purpose. We first make a global synthesis of entropy maximisation problems in the case of a single reconstruction (measure or function) from the convex analysis point of view, as well as in the framework of the embedding into the Maximum Entropy on the Mean (MEM) setting. We further propose an extension of the entropy methods for a multidimensional case.
Mathematics Subject Classification: 90C25 / 90C46 / 62G07 / 62P30
Key words: Entropy maximisation problems / Bayesian statistics / application in engineering
© The authors. Published by EDP Sciences, ROADEF, SMAI 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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