Active subspace uncertainty quantification for a polydomain ferroelectric phase-field model

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.

[1]  Heikki Haario,et al.  DRAM: Efficient adaptive MCMC , 2006, Stat. Comput..

[2]  William S. Oates,et al.  Identifiability and Active Subspace Analysis for a Polydomain Ferroelectric Phase Field Model , 2017 .

[3]  Paul G. Constantine,et al.  Active Subspaces - Emerging Ideas for Dimension Reduction in Parameter Studies , 2015, SIAM spotlights.

[4]  F. Falk Ginzburg-Landau theory of static domain walls in shape-memory alloys , 1983 .

[5]  Lider S. Leon,et al.  Analysis of a multi-axial quantum informed ferroelectric continuum model: Part 1—uncertainty quantification , 2018, Journal of Intelligent Material Systems and Structures.

[6]  Hany S. Abdel-Khalik,et al.  Hybrid reduced order modeling applied to nonlinear models , 2012 .

[7]  Max D. Morris,et al.  Factorial sampling plans for preliminary computational experiments , 1991 .

[8]  Trent Michael Russi,et al.  Uncertainty Quantification with Experimental Data and Complex System Models , 2010 .

[9]  Ralph C. Smith,et al.  Uncertainty Quantification: Theory, Implementation, and Applications , 2013 .

[10]  Norman M. Wereley,et al.  Energy Harvesting Devices Using Macro-fiber Composite Materials , 2010 .

[11]  Farrukh S. Alvi,et al.  Flow sensitive actuators for micro-air vehicles , 2011 .

[12]  Cross,et al.  Theory of tetragonal twin structures in ferroelectric perovskites with a first-order phase transition. , 1991, Physical review. B, Condensed matter.

[13]  D. Vanderbilt,et al.  First-principles investigation of ferroelectricity in perovskite compounds. , 1994, Physical review. B, Condensed matter.

[14]  Robert J. Wood,et al.  The First Takeoff of a Biologically Inspired At-Scale Robotic Insect , 2008, IEEE Transactions on Robotics.