Module 4

Probabilistic Learning in Mechanics of Materials

(Johann Guilleminot, Jianfeng Lu)

In this module, we will explore the use of probabilistic learning in the mechanics of materials. We will begin with a basic introduction to diffusion and stochastic simulations. Students will then learn about manifold learning, which is an efficient nonlinear dimension reduction technique enabling the analysis and representation of data exhibiting some geometrical structure. Students will then see how to combine this approach with Hamiltonian MCMC, with the aim of jointly sampling the inputs and outputs of a given materials model on an intrinsic manifold. Both theoretical and computational aspects will be reviewed, with an emphasis on key methodological components. Various applications will be presented, including design optimization, multiscale analysis, and uncertainty quantification.

Learning objectives: 

1. Students will be able to describe fundamental concepts and methodological components in Hamiltonian-based

sampling on manifolds;

2. Students will demonstrate the ability to apply the probabilistic learning framework to augment datasets.