Efficient searching of processing parameter space to enable inverse microstructural design of materials

Materials design can be accelerated by the use of physics-based forward models that predict the properties of new materials. In cases where the properties of the material depend on its microstructure, the models can be used as part of an optimization scheme to predict the microstructural features that are required to achieve the design objectives. Producing these microstructures, however, requires that we determine the processing parameters necessary to produce the target microstructure. Here we demonstrate the use of Bayesian optimization using simple analytic forward models to enable this inverse process design in the context of optimization of isothermal heat treatment of a commercial aluminum alloy to achieve (i) a target volume fraction of a specific intermetallic phase, (ii) a specified aluminum grain size distribution, and (iii) both objectives simultaneously. We discuss the use, and limitations, of Bayesian optimization with a scalar desirability function for solving multi-objective problems, and demonstrate Bayesian optimization with expected hypervolume improvement to determine the Pareto front describing the trade-off between multiple objectives. We compare Bayesian optimization with a genetic algorithm (NSGA-II) and show that while the two approaches produce similar Pareto fronts, the Bayesian optimization converges on the solution more quickly. We further illustrate the effect of parametric uncertainty in the forward models on the uncertainty of the Pareto front. Finally, we demonstrate experimentally that the optimized process parameters do indeed allow us to make samples with the desired microstructure.