Uncertainty Quantification in Multiscale Materials Modeling provides a complete overview of uncertainty quantification (UQ) in computational materials science. It provides practical tools and methods along with examples of their application to problems in materials modeling. UQ methods are applied to various multiscale models ranging from the nanoscale to macroscale. This book presents a thorough synthesis of the state-of-the-art in UQ methods for materials modeling, including Bayesian inference, surrogate modeling, random fields, interval analysis, and sensitivity analysis, providing insight into the unique characteristics of models framed at each scale, as well as common issues in modeling across scales.
1. Cover image - p. i 2. Title page - p. i 3. Table of Contents - p. iii 4. Mechanics of Advanced Materials Series - p. ii 5. Copyright - p. iv 6. Contributors - p. xi 7. About the Series editors - p. xv 8. Preface - p. xvii 9. 1. Uncertainty quantification in materials modeling - p. 1 10. 2. The uncertainty pyramid for electronic-structure methods - p. 41 11. 3. Bayesian error estimation in density functional theory - p. 77 12. 4. Uncertainty quantification of solute transport coefficients - p. 93 13. 5. Data-driven acceleration of first-principles saddle point and local minimum search based on scalable Gaussian processes - p. 119 14. 6. Bayesian calibration of force fields for molecular simulations - p. 169 15. 7. Reliable molecular dynamics simulations for intrusive uncertainty quantification using generalized interval analysis - p. 229 16. 8. Sensitivity analysis in kinetic Monte Carlo simulation based on random set sampling - p. 273 17. 9. Quantifying the effects of noise on early states of spinodal decomposition:: Cahn–Hilliard–Cook equation and energy-based metrics - p. 301 18. 10. Uncertainty quantification of mesoscale models of porous uranium dioxide - p. 329 19. 11. Multiscale simulation of fiber composites with spatially varying uncertainties - p. 355 20. 12. Modeling non-Gaussian random fields of material properties in multiscale mechanics of materials - p. 385 21. 13. Fractal dimension indicator for damage detection in uncertain composites - p. 421 22. 14. Hierarchical multiscale model calibration and validation for materials applications - p. 449 23. 15. Efficient uncertainty propagation across continuum length scales for reliability estimates - p. 473 24. 16. Bayesian Global Optimization applied to the design of shape-memory alloys - p. 519 25. 17. An experimental approach for enhancing the predictability of mechanical properties of additively manufactured architected materials with manufacturing-induced variability - p. 539 26. Index - p. 567
Uncertainty Quantification in Multiscale Materials Modeling provides a complete overview of uncertainty quantification (UQ) in computational materials science. It provides practical tools and methods along with examples of their application to problems in materials modeling. UQ methods are applied to various multiscale models ranging from the nanoscale to macroscale. This book presents a thorough synthesis of the state-of-the-art in UQ methods for materials modeling, including Bayesian inference, surrogate modeling, random fields, interval analysis, and sensitivity analysis, providing insight into the unique characteristics of models framed at each scale, as well as common issues in modeling across scales.
1. Cover image - p. i 2. Title page - p. i 3. Table of Contents - p. iii 4. Mechanics of Advanced Materials Series - p. ii 5. Copyright - p. iv 6. Contributors - p. xi 7. About the Series editors - p. xv 8. Preface - p. xvii 9. 1. Uncertainty quantification in materials modeling - p. 1 10. 2. The uncertainty pyramid for electronic-structure methods - p. 41 11. 3. Bayesian error estimation in density functional theory - p. 77 12. 4. Uncertainty quantification of solute transport coefficients - p. 93 13. 5. Data-driven acceleration of first-principles saddle point and local minimum search based on scalable Gaussian processes - p. 119 14. 6. Bayesian calibration of force fields for molecular simulations - p. 169 15. 7. Reliable molecular dynamics simulations for intrusive uncertainty quantification using generalized interval analysis - p. 229 16. 8. Sensitivity analysis in kinetic Monte Carlo simulation based on random set sampling - p. 273 17. 9. Quantifying the effects of noise on early states of spinodal decomposition:: Cahn–Hilliard–Cook equation and energy-based metrics - p. 301 18. 10. Uncertainty quantification of mesoscale models of porous uranium dioxide - p. 329 19. 11. Multiscale simulation of fiber composites with spatially varying uncertainties - p. 355 20. 12. Modeling non-Gaussian random fields of material properties in multiscale mechanics of materials - p. 385 21. 13. Fractal dimension indicator for damage detection in uncertain composites - p. 421 22. 14. Hierarchical multiscale model calibration and validation for materials applications - p. 449 23. 15. Efficient uncertainty propagation across continuum length scales for reliability estimates - p. 473 24. 16. Bayesian Global Optimization applied to the design of shape-memory alloys - p. 519 25. 17. An experimental approach for enhancing the predictability of mechanical properties of additively manufactured architected materials with manufacturing-induced variability - p. 539 26. Index - p. 567
