Using data to account for lack of data: Linking material informatics with stochastic analysis
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Many material systems of fundamental as well as industrial importance are significantly affected by underlying fluctuations and variations in boundary conditions, initial conditions, material property, as well as variabilities in operating and surrounding conditions. There has been increasing interest in analyzing, quantifying, and controlling the effects of such uncertain inputs on complex systems. This has resulted in the development of techniques in stochastic analysis and predictive modeling. A general application of stochastic techniques to many significant problems in engineering has been limited due to the lack of realistic, viable models of the input variability. Ideas of material informatics can be used to utilize available data about the input to construct a data-driven, computationally viable model of the input variability. This promising coupling of material informatics and stochastic analysis is investigated and some results are showcased using a simple example of analyzing diffusion in heterogeneous random media. Limited microstructural data is utilized to construct a realistic model of the thermal conductivity variability in a system. This reduced-order model then serves as the input to the stochastic partial differential equation describing thermal diffusion through random heterogeneous media.
KeywordsStochastic Analysis Sparse Grid Stochastic Partial Differential Equation Input Uncertainty Material Informatics
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