Recent progress of uncertainty quantification in small-scale materials science

This work addresses a comprehensive review of the recent efforts for uncertainty quantification in small-scale materials science. Experimental and computational studies for analyzing and designing materials in small length-scales, such as atomistic, molecular, and meso levels, have emerged substantially over the last decade. With the advancement in computational resources, uncertainty quantification has started to garner interest in the community. The effects of uncertainties have been found to be critical in numerous studies as they lead to significant deviations on the expected material response and alter the component performance. In the field of small-scale materials science, typical resources of the uncertainties are classified as: (i) inherent material stochasticity (aleatoric uncertainty) associated with processing; (ii) modeling and algorithmic variations (epistemic uncertainty) that arise from the lack of knowledge on the systems/models. The present work reviews the recent efforts in the field and categorize according to various aspects: (i) types of uncertainties, (ii) types of uncertainty quantification problems, (iii) algorithms that are used to study the uncertainties, and (iv) length-scales in different applications. The extensive discussion covers the state-of-the-art and promising future techniques and applications, including the integration of the uncertainty quantification, design, optimization and reliability methods, and uncertainty quantification in advanced manufacturing.