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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. 

The geometrical arrangement of metamaterials controls their mechanical properties, such as Young’s modulus and the shear modulus. However, optimizing the geometrical arrangement for user-defined performance criteria leads to an inverse problem that is intractable when considering numerous combinations of properties and underlying geometries. Machine-learning techniques have been proven to be effective and practical to accomplish such nonintuitive design tasks. This paper proposes an inverse design framework using conditional generative adversarial networks (CGANs) to explore and optimize two-dimensional metamaterial designs consisting of spinodal topologies, called spinodoids. CGANs are capable of solving the many-to-many inverse problem, which requires generating a group of geometric patterns of representative volume elements with target combinations of mechanical properties. The performance of the networks was validated by numerical simulations with the finite element method. The proposed inverse design framework vastly improves the efficiency of design exploration and optimization of spinodoid metamaterials. 

Microstructure-sensitive materials design has become popular among materials engineering researchers in the last decade because it allows the control of material performance through the design of microstructures. In this study, the microstructure is defined by an orientation distribution function. A physics-informed machine learning approach is integrated into microstructure design to improve the accuracy, computational efficiency, and explainability of microstructure-sensitive design. When data generation is costly and numerical models need to follow certain physical laws, machine learning models that are domain-aware perform more efficiently than conventional machine learning models. Therefore, a new paradigm called the physics-informed neural network (PINN) is introduced in the literature. This study applies the PINN to microstructure-sensitive modeling and inverse design to explore the material behavior under deformation processing. In particular, we demonstrate the application of PINN to small-data problems driven by a crystal plasticity model that needs to satisfy the physics-based design constraints of the microstructural orientation space. For the first problem, we predict the microstructural texture evolution of copper during a tensile deformation process as a function of initial texturing and strain rate. The second problem aims to calibrate the crystal plasticity parameters of the Ti-7Al alloy by solving an inverse design problem to match the PINN-predicted final texture prediction and the experimental data.