A key challenge in any of these efforts is to determine specific nanoparticle microstructures that are optimal for targeted macroscopic properties. Knowledge of such microstructures could provide new mechanistic insights, and in addition facilitate discovery of nanoparticle interactions that are most promising for experimental realization of the microstructures using inverse methods. Due to the high-dimensional nature of the relevant search spaces, which in principle includes all possible configurations of the nanoparticles, experimental screening of candidate microstructures is often practically intractable. An attractive alternative is to solve for the microstructures using a topology optimization algorithm that leverages structure-property predictions from a computationally tractable surrogate model.