@article{leon_miles_smith_oates_2019, title={Active subspace analysis and uncertainty quantification for a polydomain ferroelectric phase-field model}, volume={30}, ISSN={["1530-8138"]}, DOI={10.1177/1045389X19853636}, abstractNote={ We perform parameter subset selection and uncertainty analysis for phase-field models that are applied to the ferroelectric material lead titanate. A motivating objective is to determine which parameters are influential in the sense that their uncertainties directly affect the uncertainty in the model response, and fix noninfluential parameters at nominal values for subsequent uncertainty propagation. We employ Bayesian inference to quantify the uncertainties of gradient exchange parameters governing 180° and 90° tetragonal phase domain wall energies. The uncertainties of influential parameters determined by parameter subset selection are then propagated through the models to obtain credible intervals when estimating energy densities quantifying polarization and strain across domain walls. The results illustrate various properties of Landau and electromechanical coupling parameters and their influence on domain wall interactions. We employ energy statistics, which quantify distances between statistical observations, to compare credible intervals constructed using a complete set of parameters against an influential subset of parameters. These intervals are obtained from the uncertainty propagation of the model input parameters on the domain wall energy densities. The investigation provides critical insight into the development of parameter subset selection, uncertainty quantification, and propagation methodologies for material modeling domain wall structure evolution, informed by density functional theory simulations. }, number={14}, journal={JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES}, author={Leon, Lider S. and Miles, Paul R. and Smith, Ralph C. and Oates, William S.}, year={2019}, month={Aug}, pages={2027–2051} }
 @article{leon_smith_miles_oates_2018, title={Active Subspace Uncertainty Quantification for a Polydomain Ferroelectric Phase-Field Model}, volume={10596}, ISSN={["1996-756X"]}, DOI={10.1117/12.2297207}, abstractNote={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.}, journal={BEHAVIOR AND MECHANICS OF MULTIFUNCTIONAL MATERIALS AND COMPOSITES XII}, author={Leon, Lider S. and Smith, Ralph C. and Miles, Paul and Oates, William S.}, year={2018} }
 @article{leon_smith_oates_miles_2017, title={Global Sensitivity Analysis for a Quantum Informed Ferroelectric Phase Field Model}, volume={10165}, ISSN={["1996-756X"]}, DOI={10.1117/12.2259945}, abstractNote={We consider global sensitivity analysis (GSA) for correlated parameters in a continuum phase-field model for ferroelectric materials. The model was previously calibrated using density functional theory (DFT) simulations. For single domain ferroelectric lead titanate crystals, GSA is employed to rank the sensitivity of phenomenological parameters governing the Landau energy surface. The sensitivity analysis is based on Sobol’s variance-based decomposition in which the component functions of the high-dimensional representation (HDMR) of the model are computed analytically. For the subset of parameters that are most correlated, high-order component functions and sensitivity indices are found to be significant.}, journal={BEHAVIOR AND MECHANICS OF MULTIFUNCTIONAL MATERIALS AND COMPOSITES 2017}, author={Leon, Lider S. and Smith, Ralph C. and Oates, William S. and Miles, Paul}, year={2017} }
 @inproceedings{leon_smith_oates_miles_2017, title={Identifiability and active subspace analysis for a polydomain ferroelectric phase field model}, DOI={10.1115/smasis2017-3845}, abstractNote={We consider subset selection and active subspace techniques for parameters in a continuum phase-field polydomain model for ferroelectric materials. This analysis is necessary to mathematically determine the parameter subset or subspace critically affecting the response, prior to model calibration using either experimental or synthetic data constructed using density functional theory (DFT) simulations. For the 180° domain wall model, we employ identifiability analysis using a Fisher information matrix methodology, and subspace selection to determine the active subspace. We demonstrate the implementation and interpretation of techniques that accommodate the model structure and discuss results in the context of identifiable parameter subsets and active subspaces quantifying the strongest influence on the model output. Our results indicate that the governing domain wall gradient energy exchange parameter is most identifiable.}, booktitle={Proceedings of the asme conference on smart materials adaptive}, author={Leon, L. S. and Smith, Ralph and Oates, W. S. and Miles, P.}, year={2017} }
 @article{miles_leon_smith_oates_2017, title={Uncertainty Analysis of Continuum Phase Field Modeling in 180 degrees Domain Wall Structures}, volume={10165}, ISSN={["1996-756X"]}, DOI={10.1117/12.2260130}, abstractNote={The evolution and formation of domain structures in ferroelectric materials is modeled using a continuum phase field approach and compared with density functional theory (DFT) using Bayesian uncertainty analysis. These simulations are carried out on the ferroelectric, lead titanate. Self-consistency between DFT and the continuum approach is advantageous when computing polydomain structures and domain wall dynamics. There is uncertainty in the phenomenological parameters related to the Landau energy, electrostriction, and twinned domain wall energy in single and polydomain ferroelectric crystals. To quantify the model parameter uncertainty associated with the phase field model, Bayesian statistics were used. Specifically, we will focus on estimating the value of the exchange parameters associated with polarization gradients. The phase field model predictions for the 180° domain wall energy are calibrated based upon DFT calculations. Model predictions of domain wall size are found to be on the same order as DFT calculations.}, journal={BEHAVIOR AND MECHANICS OF MULTIFUNCTIONAL MATERIALS AND COMPOSITES 2017}, author={Miles, Paul and Leon, Lider and Smith, Ralph and Oates, William}, year={2017} }
 @inproceedings{miles_oates_leon_smith_2017, title={Uncertainty analysis of ferroelectric polydomain structures}, DOI={10.1115/smasis2017-3916}, abstractNote={Ferroelectric materials exhibit strong electromechanical behavior which has led to the production of a wide variety of adaptive structures and intelligent systems, ranging from structural health monitoring sensors, energy harvesting circuits, and flow control actuators. Given the large number of applications, accurate prediction of ferroelectric materials constitutive behavior is critical. This presents many challenges, including the need to predict behavior from electronic structures up to macroscropic continuum. Many of the structure-property relations in these materials can be accurately calculated using density functional theory (DFT). However, DFT is not necessarily conducive to the large scale computations required to solve these problems on a continuum scale. Introducing a phase field polarization order parameter is an alternative approach, which provides a means to simulate the length scale gap between nano- and microscale domain structure evolution. The introduction of the phase field approximation results in uncertainty. Bayesian statistical analysis is an ideal tool for quantifying the uncertainty associated with the continuum phase field model parameters. Analyses of monodomain structures allows for identification of Landau energy and electrostrictive stress parameters. Identifying the exchange parameters, which are proportional to the polarization gradients, requires consideration of polydomain structures. This is a nontrivial problem as domain wall structures are fully coupled between the Landau energy, electrostrictive, and exchange parameters. Accurately quantifying the uncertainty in the phase field parameters will provide insight into the nonlinear constitutive behavior.}, booktitle={Proceedings of the asme conference on smart materials adaptive}, author={Miles, P. and Oates, W. and Leon, L. and Smith, Ralph}, year={2017} }
 @article{sawyer_evans_wilson_beesley_leon_eklund_croom_pegram_2016, title={Development of a human physiologically based pharmacokinetic (PBPK) model for dermal permeability for lindane}, volume={245}, ISSN={["1879-3169"]}, DOI={10.1016/j.toxlet.2016.01.008}, abstractNote={Lindane is a neurotoxicant used for the treatment of lice and scabies present on human skin. Due to its pharmaceutical application, an extensive pharmacokinetic database exists in humans. Mathematical diffusion models allow for calculation of lindane skin permeability coefficients using human kinetic data obtained from in vitro and in vivo experimentation as well as a default compound-specific calculation based on physicochemical characteristics used in the absence of kinetic data. A dermal model was developed to describe lindane diffusion into the skin, where the skin compartment consisted of homogeneous dermal tissue. This study utilized Fick's law of diffusion along with chemical binding to protein and lipids to determine appropriate dermal absorption parameters which were then incorporated into a physiologically based pharmacokinetic (PBPK) model to describe in vivo kinetics. The estimation of permeability coefficients using chemical binding in combination with in vivo data demonstrates the advantages of combining physiochemical properties with a PBPK model to predict dermal absorption.}, journal={TOXICOLOGY LETTERS}, author={Sawyer, Megan E. and Evans, Marina V. and Wilson, Charles A. and Beesley, Lauren J. and Leon, Lider S. and Eklund, Chris R. and Croom, Edward L. and Pegram, Rex A.}, year={2016}, month={Mar}, pages={106–109} }
 @article{oates_miles_leon_smith_2016, title={Uncertainty analysis of continuum scale ferroelectric energy landscapes using density functional theory}, volume={9800}, ISSN={["1996-756X"]}, DOI={10.1117/12.2219273}, abstractNote={Density functional theory (DFT) provides exceptional predictions of material properties of ideal crystal structures such as elastic modulus and dielectric constants. This includes ferroelectric crystals where excellent predictions of spontaneous polarization, lattice strain, and elastic moduli have been predicted using DFT. Less analysis has focused on quantifying uncertainty of the energy landscape over a broad range of polarization states in ferroelectric materials. This is non-trivial because the degrees of freedom contained within a unit cell are reduced to a single vector order parameter which is normally polarization. For example, lead titanate contains five atoms and 15 degrees of freedom of atomic nuclei motion which contribute to the overall unit cell polarization. Bayesian statistics is used to identify the uncertainty and propagation of error of a continuum scale, Landau energy function for lead titanate. Uncertainty in different parameters is quantified and this uncertainty is propagated through the model to illustrate error propagation over the energy surface. Such results are shown to have an impact in integration of quantum simulations within a ferroelectric phase field continuum modeling framework.}, journal={BEHAVIOR AND MECHANICS OF MULTIFUNCTIONAL MATERIALS AND COMPOSITES 2016}, author={Oates, William S. and Miles, Paul and Leon, Lider and Smith, Ralph}, year={2016} }