Preliminary list of abstracts

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Uncertainty quantification in random heterogeneous media
Keywords: Stochastic PDEs; Uncertainty quantification
Tue, 16:30--17:15
  • Zabaras, Nicholas J. (Sibley School of Mechanical and Aerospace Engineering, Cornell University, United States)

Predictive modeling of physical processes in heterogeneous materials requires innovations in mathematical and computational thinking. While recent multiscale approaches have been successful in modeling the effects of microstructure to macroscopic response, a significant grand challenge remains in understanding the effects of microstructural and other uncertainties in characterization of properties and in the design of heterogeneous materials. To address these problems, we are developing a mathematical framework that provides 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: (I) 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 a low-complexity surrogate model of the high-dimensional stochastic multiscale system under consideration. We will discuss ideas based on manifold learning, kernel PCA, locally weighted projection regression methods in high dimensions, sparse Bayesian kernel techniques, and others. A number of examples will be discussed in the data-driven representation of random heterogeneous media and in modeling physical processes (deformation, thermal/hydrodynamic transport, etc.) in such media. We will emphasize both the underlying mathematical challenges but also the significant technological impact of predictive modeling in random heterogeneous media.