Mohammad Motamed
Department of Mathematics and Statistics, The University of New Mexico, USA
Predictive computational science is an emerging discipline concerned with assessing the predictability of mathematical and computational tools, particularly in the presence of uncertainty and limited information. In this talk, I will present a comprehensive predictive methodology embedded in a new hybrid fuzzy-stochastic framework to predict physical events described by partial differential equations (PDEs) and subject to both random (aleatoric) and non-random (epistemic) uncertainty. In the new framework the uncertain input parameters are characterized by random fields with fuzzy moments. This will result in a new class of PDEs with hybrid fuzzy-stochastic parameters, coined fuzzy-stochastic PDEs, for which forward and inverse problems need to be solved. I will demonstrate the importance and feasibility of the new methodology by applying it to a complex problem: prediction of the response of materials with hierarchical microstructure to external forces. This model problem will serve as an illustrative example, one that cannot be tackled by today's Uncertainty Quantification methodologies.