A Bayesian Approach to Morphological Models Characterization

Abstract

Morphological models are commonly used to describe microstructures observed in heterogeneous materials. Usually, these models depend upon a set of parameters that must be chosen carefully to match experimental observations conducted on the microstructure. A common approach to perform the parameters determination is to try to minimize an objective function, usually taken to be the discrepancy between measurements computed on the simulations and on the experimental observations, respectively. In this article, we present a Bayesian approach for determining the parameters of morphological models, based upon the definition of a posterior distribution for the parameters. A Monte Carlo Markov Chains (MCMC) algorithm is then used to generate samples from the posterior distribution and to identify a set of optimal parameters. We show on several examples that the Bayesian approach allows us to properly identify the optimal parameters of distinct morphological models and to identify potential correlations between the parameters of the models.

A supervised algorithm entirely trained on a synthetic dataset to segment granular suspension images

“…In addition, the annotation itself is error prone due to the inevitable loss of attention of the operator in charge of annotating the images. The main originality of our approach is that we entirely trained the network on a series of synthetic images generated with morphological models (Figliuzzi, 2019;Figliuzzi et al, 2021;Jeulin, 2021;Stoyan et al, 2013), commonly used to simulate micro-structures in materials engineering (Bortolussi et al, 2018;Figliuzzi et al, 2016), rather than on images of real experiments. With our approach of artificial synthesis of the ground truth, the positions and sizes of the particles are known by construction, which allows us to get rid of the difficulty of obtaining a reliable learning database 1 .…”