Research Fellows Directory
Professor Nicholas Zabaras
University of Warwick
The main objective of our work is to quantify how lack of information on material properties, material microstructure, process conditions, etc. propagated to properties we predict (e.g. strength of an alloy) or the performance of materials we design. Our approach is an interdisciplinary one using elements of mathematics, statistics, scientific computing and materials physics.
Predictive modelling and design of materials gives rise to unique mathematical and computational challenges including (i) Modelling of hierarchical random heterogeneous material structures; (ii) Propagating uncertainties in a quantifiable manner across spatial and temporal length scales (stochastic coarse graining); (iii) Addressing the curse of stochastic dimensionality; (iv) Addressing the phenomenology typical of most materials science models; (v) Modelling failure and rare events in random media; and many more.
We advocate an information theoretic approach to address some of these challenges. In particular, we develop data-driven models of material structure, forward uncertainty propagation in high dimensions using limited data, variational approaches to stochastic coarse graining, and quantifying epistemic uncertainty when using surrogate models. Our approaches are utilizing advances in machine learning e.g. probabilistic graphical models are being used to model multiscale/multiphysics materials problems.
With synergistic developments in materials physics, computational mathematics/statistics, and machine learning there is potential for developing data-driven materials models that allow us to understand where observable variabilities in properties arise and provide means to control them for accelerated materials design. This is important for an accelerated insertion of new materials, for virtual testing of materials devices and products and other. This is significant not only from an intelectual point of view but mainly for its potential impact in manufacturing.