  In this study, a framework for the multi-objective materials discovery based
on Bayesian approaches is developed. The capabilities of the framework are
demonstrated on an example case related to the discovery of precipitation
strengthened NiTi shape memory alloys with up to three desired properties. In
the presented case the framework is used to carry out an efficient search of
the shape memory alloys with desired properties while minimizing the required
number of computational experiments. The developed scheme features a Bayesian
optimal experimental design process that operates in a closed loop. A Gaussian
process regression model is utilized in the framework to emulate the response
and uncertainty of the physical/computational data while the sequential
exploration of the materials design space is carried out by using an optimal
policy based on the expected hyper-volume improvement acquisition function.
This scalar metric provides a measure of the utility of querying the materials
design space at different locations, irrespective of the number of objectives
in the performed task. The framework is deployed for the determination of the
composition and microstructure of precipitation-strengthened NiTi shape memory
alloys with desired properties, while the materials response as a function of
microstructure is determined through a thermodynamically-consistent
micromechanical model.
