Microstructure design using machine learning generated low dimensional and continuous design space

Abstract

The cornerstone of materials design is the design space used in solving materials related optimization problems. Materials design strategies often involve evaluating properties of materials with selected design variables. Because a microstructure comprises a high dimensional data, dimensionality reduction using principal component analysis or multi-dimensional scaling has become a common practice in generating low dimensional design variables. Unfortunately, generation of microstructures is not guaranteed using design variables formulated using popular dimensionality reduction techniques. These design variables are limited to the initial dataset used for dimensionality reduction, resulting in a discontinuous design space. This shortcoming severely constrains design flexibility and can hamper the performance of design strategies. To address this limitation, we propose the use of the latent space of a convolutional autoencoder trained with synthetic dual phase (DP) microstructures as low dimensional and continuous design space. Once the design space is established, Bayesian optimization is adopted to search for optimal microstructures that exhibit maximal tensile strength. The strength of each microstructure is approximated using microstructure based finite element method. To take full advantage of the continuous design space, a second Bayesian optimization with a refined search space is adopted. The second Bayesian optimization resulted in higher maximum strength value and fewer number of data necessary to find the optimal microstructure compared to Bayesian optimization without search space refinement. Furthermore, multiple microstructures exhibiting strengths comparable to that of the optimal microstructure can be identified within the refined search space, providing significant flexibility in microstructure design.