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 quantum scale at which calculations take place. A necessary analysis is to determine how the uncertainty in the response can be attributed to the uncertainty in the model inputs or parameters. A second analysis is to identify active subspaces within the original parameter space, which quantify directions in which the model response varies most dominantly, thus reducing sampling effort and computational cost. In this investigation, we identify an active subspace for a poly-domain ferroelectric phase-field model. Using the active variables as our independent variables, we then construct a surrogate model and perform Bayesian inference. Once we quantify the uncertainties in the active variables, we obtain uncertainties for the original parameters via an inverse mapping. The analysis provides insight into how active subspace methodologies can be used to reduce computational power needed to perform Bayesian inference on model parameters informed by experimental or simulated data.
Lider S. Leon, Ralph C. Smith, Paul Miles, and William S. Oates, "Active subspace uncertainty quantification for a polydomain ferroelectric phase-field model," Proc. SPIE 10596, Behavior and Mechanics of Multifunctional Materials and Composites XII, 105960T (Presented at SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring: March 06, 2018; Published: 22 March 2018); https://doi.org/10.1117/12.2297207.
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