Uncertainty Quantification in Multiscale Materials Modeling

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.

Synthesizes available UQ methods for materials modelingProvides practical tools and examples for problem solving in modeling material behavior across various length scalesDemonstrates UQ in density functional theory, molecular dynamics, kinetic Monte Carlo, phase field, finite element method, multiscale modeling, and to support decision making in materials designCovers quantum, atomistic, mesoscale, and engineering structure-level modeling and simulation

1. Uncertainty quantification in materials modeling
2. The uncertainty pyramid for electronic-structure methods
3. Bayesian error estimation in density functional theory
4. Uncertainty quantification of solute transport coefficients
5. Data-driven acceleration of first-principles saddle point and local minimum search based on scalable Gaussian processes
6. Bayesian calibration of force fields for molecular simulations
7. Reliable molecular dynamics simulations for intrusive uncertainty quantification using generalized interval analysis
8. Sensitivity analysis in kinetic Monte Carlo simulation based on random set sampling
9. Quantifying the effects of noise on early states of spinodal decomposition: CahneHilliardeCook equation and energy-based metrics
10. Uncertainty quantification of mesoscale models of porous uranium dioxide
11. Multiscale simulation of fiber composites with spatially varying uncertainties
12. Modeling non-Gaussian random fields of material properties in multiscale mechanics of materials
13. Fractal dimension indicator for damage detection in uncertain composites
14. Hierarchical multiscale model calibration and validation for materials applications
15. Efficient uncertainty propagation across continuum length scales for reliability estimates
16. Bayesian Global Optimization applied to the design of shape-memory alloys
17. An experimental approach for enhancing the predictability of mechanical properties of additively manufactured architected materials with manufacturing-induced variability