Uncertainty quantification in multiscale materials modeling /
edited by Yan Wang and David L. McDowell.
- 1 online resource (xviii, 586 pages) : illustrations
- Elsevier series in mechanics of advanced materials .
- Elsevier series in mechanics of advanced materials. .
Includes bibliographical references and index.
Front Cover -- Uncertainty Quantification in Multiscale Materials Modeling -- Mechanics of Advanced Materials Series -- Series editor-in-chief: Vadim V. Silberschmidt -- Series editor: Thomas B�ohlke -- Series editor: David L. McDowell -- Series editor: Zhong Chen -- Uncertainty Quantification in Multiscale Materials Modeling -- Copyright -- Contents -- Contributors -- About the Series editors -- Editor-in-Chief -- Series editors -- Preface -- 1 -- Uncertainty quantification in materials modeling -- 1.1 Materials design and modeling -- 1.2 Sources of uncertainty in multiscale materials modeling 1.2.1 Sources of epistemic uncertainty in modeling and simulation -- 1.2.2 Sources of model form and parameter uncertainties in multiscale models -- 1.2.2.1 Models at different length and time scales -- 1.2.3 Linking models across scales -- 1.3 Uncertainty quantification methods -- 1.3.1 Monte Carlo simulation -- 1.3.2 Global sensitivity analysis -- 1.3.3 Surrogate modeling -- 1.3.4 Gaussian process regression -- 1.3.5 Bayesian model calibration and validation -- 1.3.6 Polynomial chaos expansion -- 1.3.7 Stochastic collocation and sparse grid -- 1.3.8 Local sensitivity analysis with perturbation 1.3.9 Polynomial chaos for stochastic Galerkin -- 1.3.10 Nonprobabilistic approaches -- 1.4 UQ in materials modeling -- 1.4.1 UQ for ab initio and DFT calculations -- 1.4.2 UQ for MD simulation -- 1.4.3 UQ for meso- and macroscale materials modeling -- 1.4.4 UQ for multiscale modeling -- 1.4.5 UQ in materials design -- 1.5 Concluding remarks -- Acknowledgments -- References -- 2 -- The uncertainty pyramid for electronic-structure methods -- 2.1 Introduction -- 2.2 Density-functional theory -- 2.2.1 The Kohn-Sham formalism -- 2.2.2 Computational recipes -- 2.3 The DFT uncertainty pyramid 2.3.1 Numerical errors -- 2.3.2 Level-of-theory errors -- 2.3.3 Representation errors -- 2.4 DFT uncertainty quantification -- 2.4.1 Regression analysis -- 2.4.2 Representative error measures -- 2.5 Two case studies -- 2.5.1 Case 1: DFT precision for elemental equations of state -- 2.5.2 Case 2: DFT precision and accuracy for the ductility of a W-Re alloy -- 2.6 Discussion and conclusion -- Acknowledgment -- References -- 3 -- Bayesian error estimation in density functional theory -- 3.1 Introduction -- 3.2 Construction of the functional ensemble -- 3.3 Selected applications -- 3.4 Conclusion