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Lider Leon, North Carolina State University, presents this seminar.

Ferroelectric materials have powerful properties that make them useful for employment in advanced engineering applications. Quantum-informed ferroelectric phase-field models capable of predicting material behavior are necessary for facilitating the development and production of many adaptive structures and intelligent systems. Uncertainty is present in these models given the scale at which molecular dynamic density functional theory (DFT) calculations take place to inform a continuum model. An initial necessary analysis is to determine how the uncertainty in the model response can be attributed to the uncertainty in the inputs or parameters. A second analysis is to identify active subspaces within the original parameter space, which quantify directions in which the response varies most dominantly, thus reducing sampling effort for Bayesian statistical inference.

In this talk, we introduce the general properties of ferroelectric materials, while presenting a number of applications where these materials are employed. We introduce the models used to characterize material evolution and the techniques used for model simulation. We additionally present parameter subset selection and active subspace methodologies, and their implementation for a ferroelectric phase-field model applied to lead titanate. We use these methods to determine the most sensitive parameters, while fixing the insignificant ones at nominal values, to perform uncertainty analysis and propagation of the underlying model. To verify our findings, we compare the results of uncertainty propagation using the original set of parameters, with the results when using a (possible) reduced set of parameters. The analysis provides insight into how parameter subset selection is used to reduce sampling effort prior to performing Bayesian uncertainty quantification informed by experimental or simulated data.