Energetic upscaling strategy for grain growth. II: Probabilistic macroscopic model identified by Bayesian techniques

This paper is the second part of an energetic upscaling strategy to simulate grain growth at macroscopic scale with state variables that contain statistical descriptors structure. The first was dedicated derivation a fast mesoscopic model based on orientated tessellation updating method, which consists in succession Voronoi-Laguerre tessellations obtained by establishing evolution law directly parameters defining tessellations. In this contribution, final step detailed deriving evolutions laws representing distributions approach relies free energy and dissipation potentials are identified not axiomatically, but using large database computations. found be purely deterministic, although necessitates introduce probabilistic framework. Indeed, epistemic uncertainty arises due loss information reduction amount data between (i.e., several states can share same state). Classical Bayesian inference has been used identify probability density functions associated uncertainty. From computational point view, work very short computation time, while processing rich about structure, such as indicators boundary character distribution. resulting stochastic compared particular evolutions, good agreement observed. However, still requires experimental validation.