Accelerated materials design using batch Bayesian optimization: A case study for solving the inverse problem from materials microstructure to process specification

Microstructure-based process design is one of the main ingredients for materials design, under the integrated computational materials engineering paradigm, which relies on inverting process-structure–property linkages. The specific inverse problem connecting microstructure to processing conditions is exceedingly difficult to solve, even in a computational setting. The difficulty arises from the challenges associated with properly representing the microstructure space as well as the computational cost of the simulations used to connect process conditions to microstructure evolution. In this work, we attempt to invert a process-microstructure problem by implementing and deploying a search scheme based on multi-scale batch Bayesian optimization. We employ this framework to efficiently navigate the microstructure manifold in two examples involving phase-field simulations. In these examples, the volume fraction and characteristic length scale of phases resulting from spinodal decompositions are considered in different objective functions to find synthetic target microstructures. We show how this batch Bayesian optimization can be used to efficiently uncover process-microstructure connections through optimal parallel querying of the process space, providing a new pathway for solving inverse problems in materials design.