Bregman divergences for physically informed discrepancy measures for learning and computation in thermomechanics - Andrieux, Stéphane (Comptes Rendus. Mécanique)
With view on the context of convex thermomechanics, we propose tools based on the concept of Bregman divergence, a notion introduced in the 1960s and used in learning and optimization as well. This study is motivated by the need of “discrepancy measures” between physically constrained fields that are used both in traditional algorithms, analysis methods and data driven modelling or applications as well.We give also a characterization of symmetrical Bregman divergences through their generating functions which can only be quadratic forms. Some properties of the Bregman divergence and the introduced concept of Bregman Gap between couples of dual quantities are given, and some existing errors in thermomechanics are recovered. Exploiting the framework of Standard Generalized Materials, we give a set of generating functions for a large range of applications, including coupled multi-physics. Finally some results useful for computational geometry are detailed.