Analysis of a multi-axial quantum-informed ferroelectric continuum model: Part 2—sensitivity analysis

Abstract

We illustrate the use of global sensitivity analysis, and a parameter subset selection algorithm based on local sensitivity analysis, to quantify the relative influence of parameters in polarization and electrostrictive energy relations for a quantum-informed, single-domain, ferroelectric material model. A motivating objective is to determine which parameters are identifiable or influential in the sense that they are uniquely determined by density functional theory–generated data. Noninfluential parameters will be fixed at nominal values for subsequent Bayesian inference, uncertainty propagation, and material design since variations in these parameters are minimally reflected in responses. Whereas global sensitivity analysis is typically based on the assumption of mutually independent, uniformly distributed parameters, we demonstrate that inherent parameter correlations must be accommodated to achieve correct interpretations of parameter influence. For the considered energy functionals, we demonstrate that all of the parameters are influential and will be informed by density functional theory–simulated data.

Ranking non-pharmaceutical interventions against Covid-19 global pandemic using global sensitivity analysis—Effect on number of deaths

“…References [33] , [35] , [40] , [64] , [66] , [67] provide detailed information on different numerical implementations of these sensitivity indices. We have implemented an in-house code on MATLAB and the algorithm is described in [35] , [36] . The current approach utilizes model calculations to obtain first order, second order and total order Sobol’ indices.…”

“…Global sensitivity methods can be used for both linear and nonlinear models. Most sensitivity analysis literature uses local sensitivity because it is simple and computationally efficient [30] , [33] , [34] , [35] , [36] , [37] . According to [30] , most of the outcomes and suggestions of such studies are erroneous and misleading.…”

Bayesian inference and uncertainty propagation using efficient fractional-order viscoelastic models for dielectric elastomers

“…This is accomplished by a systematic comparison of the eigenvalues of the Fisher Information matrix. Details of the algorithm can be found in Quaiser and Mönnigmann (2009) and Leon et al (2018). Consider the sensitivity matrix of the form…”

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

“…The available data for the 180°and 90°total domain wall energies are, respectively, reported to be E Ã 1808 = 132 mJ=m 2 and E Ã 908 = 50 mJ=m 2 from the DFT studies and Landau-Ginzburg theory analysis in Meyer and Vanderbilt (2002) and Stemmer et al (1995). As both are scalar valued, we employ the characterized uncertainties for the Landau phenomenological parameters and electrostrictive coefficients quantified in previous studies of single-domain structure evolution for PbTiO 3 (Leon et al, 2018b;Miles et al, 2018). The corresponding nominal values and standard deviations from the single-domain uncertainty analysis are presented in Table 2.…”

“…These methods are also advantageous for determining noninfluential or unidentifiable parameters, which can be fixed at nominal values for model calibration and uncertainty propagation. For a more detailed discussion on identifiable and influential parameters, we refer the reader to sources including Leon et al (2018b) and Smith (2014). In the context of our problem, we use the Fisher information-based parameter subset selection as this requires a smaller number of function evaluations to determine an identifiable subset of parameters.…”