Uncertainty is a critical element in computational materials science. From the experimental perspective, the sources of uncertainty include measurement errors caused by instrument, operator, and sensing models, as well as the curve fitting in determining the parameters of constitutive material models. From the computational perspective, the choice of material models is a source of model-form uncertainty, whereas the parameters used in these constitutive material models are sources of parameter uncertainty. Both the model-form and parameter uncertainties can be considered as epistemic uncertainty, which is reducible as the knowledge about the material advances. On the other hand, irreducible or aleatory uncertainty originates from the random distribution of materials because of the nature of statistical thermodynamics. Thus, uncertainty quantification (UQ) is an important aspect in integrated computational materials engineering (ICME) tools for the credible predictions of physical quantities of interests. The major challenges of UQ in materials modeling are the curse of dimensionality and computational complexity. In this research, efficient UQ methods are developed for both forward uncertainty propagation and prediction in ICME tools and the inverse process of materials design and optimization. A temporal-upscaling stochastic reduced-order model is developed to accelerate the uncertainty propagation beyond the time-scale limitation in simulations. The proposed method is demonstrated using kinetic Monte Carlo, molecular dynamics, and phase field simulations in the microstructural evolution problem. The stochastic collocation method is applied to study the effects of processing and thermodynamic parameters and efficiently quantify uncertainty in dendritic growth. It is demonstrated with the solidification process of Al-4wt%Cu using phase field model. For materials design and optimization under uncertainty, Bayesian optimization is extended to solve large-scale problems. A novel and accelerated Bayesian optimization method is proposed to tackle the mixed-integer optimization under known and unknown constraints, based on computationally expensive high-fidelity simulations through the parallel usage of high-performance computing architecture. The proposed batch parallel Bayesian optimization method is demonstrated using several design optimization examples, including fractal metamaterials and structures.
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