Bayesian inference of granular mesostructures: the identifiability and interplay with grain properties

Granular materials exhibit scale-dependent properties. The interplay between the structure of a representative volume element (or mesostructure) and the particle properties determine the macroscopic response of granular materials. The discrete element method (DEM) predicts complex macroscopic constitutive behavior from interparticle contacts and the mesostructure evolution. The identification of contact parameters is often treated as an inverse problem. However, uncertainties on the mesostructure are rarely considered, due to the high computational cost. We use Sequential Monte Carlo (SMC) filtering to quantify uncertainties on the contact parameters and mesostructure and train machine learning models to effectively learn and sample from contact-mesostructure correlations.

In this talk, we revisit the multi-level Bayesian calibration approach that is used to identify DEM parameters [1]. We class the inference algorithm into two processes namely the filtering phase and the sampling phase. At the core of the filtering phase is the iterative Sequential Monte Carlo (SMC) which learns a proposal distribution by minimizing the associate uncertainty. Compared to conventional SMC, where random perturbations are used to evolve a system in time, a sampling phase is employed, moving from a discrete distribution (of simulated data) to a continuous distribution (of parameters), by training a Gaussian Mixture Model (GMM). Next, we show how the Bayesian calibration algorithm is used to extend the parameter identification problem to also include the particle size distribution (PSD) and solid volume fraction as parameters [2]. The result is a set of multi-mode distributions of contact and mesostructure parameters which are iteratively approximated and sampled until convergence. The Bayesian calibration process of the mesostructure is studied using a synthesized triaxial response as the ground truth. Satisfactory macro responses are achieved for dense and loose samples, but due to the interdependence between parameters, dense samples are more prone to converge to local minima. Finally, my current research involves granular systems moving from solid to fluid and back. An overview will be given on how Bayesian statistics will be used to quantify the uncertainty between various continuum methods.