In order to find these improved solutions, the optimization algorithm searches widely and finds a number of qualitatively distinct minima. The optimization trajectories, as well as the optimization trajectory from the simulation-only optimization against the same training set, are shown in Figure . In comparison to the simulation-only optimization, shown in brown, the replicates of our multi-fidelity optimization searches the parameter space much more broadly. Particularly, the values of oxygen and carbon parameters stay within a narrow range in the simulation-only optimization, but vary widely with our multi-fidelity technique.