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IAMCS Workshop in Large-Scale Inverse Problems and Uncertainty Quantification

Nicholas Zabaras, Cornell University
Model Reduction of Stochastic Systems in Random Heterogeneous Media


Predictive modeling of physical processes in heterogeneous media requires innovations in mathematical and computational thinking. While recent multiscale approaches have been successful in modeling the effects of fine scales to macroscopic response, a significant grant challenge remains in understanding the effects of topological uncertainties in characterization of properties and in predictive modeling of processes in heterogeneous media. To address these problems, we need a paradigm shift in the predictive modeling of complex systems in the presence of uncertainties in order to address two major limitations in modeling stochastic PDEs: (1) The stochastic inputs are mostly based on ad hoc models, and (2) The number of independent stochastic parameters is typically very high. To address the former, we are developing non-linear data-driven model reduction strategies to utilize experimentally available information based on low-order realistic models of input uncertainties. To address the latter, we are developing low-complexity surrogate models of the high-dimensional stochastic multiscale system under consideration. A number of examples will be discussed in the data-driven representation of random heterogeneous media and in modeling physical processes in such media.