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Identifying the key microstructure representations is crucial for computational materials design (CMD). However, existing microstructure characterization and reconstruction (MCR) techniques have limitations to be applied for microstructural materials design. Some MCR approaches are not applicable for microstructural materials design because no parameters are available to serve as design variables, while others introduce significant information loss in either microstructure representation and/or dimensionality reduction. In this work, we present a deep adversarial learning methodology that overcomes the limitations of existing MCR techniques. In the proposed methodology, generative adversarial networks (GAN) are trained to learn the mapping between latent variables and microstructures. Thereafter, the low-dimensional latent variables serve as design variables, and a Bayesian optimization framework is …