Abstract:
Random media and the process-structure-property chain generally define complex,
high-dimensional and stochastic materials systems, posing a challenging setting for
any prediction or optimization task. In this thesis, we pursue a Bayesian approach for
learning and predicting the behavior of such systems, leveraging probabilistic machine
learning methods to identify their effective, coarse-grained properties. A particular
focus will be on limiting and mitigating the dependence on labeled data due to the
computational cost of their procurement (through established numerical discretization
techniques). We achieve the prediction of high-dimensional stochastic systems defined
by random media in the small-data domain by exploiting concepts such as physics-
informed learning, active learning and semi-supervised learning. In addition to the
data-parsimonious prediction of effective physical properties and behavior of random
media, we also demonstrate the full stochastic inversion of the entire process-structure-
property chain in a high-dimensional setting, thereby enabling the identification of
optimal process parameters for computational materials design problems.