Exploration of the Underlying Space in Microscopic Images via Deep Learning for Additively Manufactured Piezoceramics.

There has been a surge of interest in applying deep learning (DL) to microstructure generation and materials design. However, existing DL-based methods are generally limited in generating (1) microstructures with high resolution, (2) microstructures with high variability, (3) microstructures with guaranteed periodicity, and (4) highly controllable microstructures. In this study, a DL approach based on a stacked generative adversarial network (StackGAN-v2) is proposed to overcome these shortcomings. The presented modeling approach can reconstruct high-fidelity microstructures of additively manufactured piezoceramics with different resolutions, which are statistically equivalent to original microstructures either experimentally observed or numerically predicted. Advantages of the proposed modeling approach are also illustrated in terms of its capability in controlling the probability density function (PDF) of grain size, grain orientation, and micropore in a large space, which would have significant benefits in exploring the effects of these microstructure features on the piezoelectricity of piezoceramics. In the meantime, periodicity of the microstructures has been successfully introduced in the developed model, which can critically reduce the simulation volume to be considered as a representative volume element (RVE) during computational calculation of piezoelectric properties. Therefore, this DL approach can significantly accelerate the process of designing optimal microstructures when integrating with computational methods (e.g., fast Fourier spectral iterative perturbation (FSIPM)) to achieve desired piezoelectric properties. The proposed DL-based method is generally applicable to optimal design of a variety of periodic microstructures, allowing for maximum explorations of design spaces and fine manipulations of microstructural features.