Bayesian Deep Learning Framework for Uncertainty Quantification in Stochastic Partial Differential Equations

Jung, Jeahan; Shin, Hyomin; Choi, Minseok

doi:10.1137/23m1560574

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2024

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Cited by 3 publications

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Uncertainty Quantification of Microstructures: A Perspective on Forward and Inverse Problems for Mechanical Properties of Aerospace Materials

Billah,

Elleithy,

Khan

et al. 2024

Adv Eng Mater

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In this review, state‐of‐the‐art studies on the uncertainty quantification (UQ) of microstructures in aerospace materials is examined, addressing both forward and inverse problems. Initially, it introduces the types of uncertainties and UQ algorithms. In the review, the forward problem of uncertainty propagation in process–structure and structure–property relationships is then explored. Subsequently, the inverse UQ problem, also known as the design under uncertainty problem, is discussed focusing on structure–process and property–structure linkages. Herein, the review concludes by identifying gaps in the current literature and suggesting key areas for future research, including multiscale topology optimization under uncertainty, implementing physics‐informed neural networks to UQ problems, investigating the effects of uncertainty on extreme mechanical behavior, reliability‐based design, and UQ in additive manufacturing.

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