Benchmarking inverse optimization algorithms for materials design

Machine learning-based inverse materials discovery has attracted enormous attention recently due to its flexibility in dealing with black box models. Yet, many metaheuristic algorithms are not as widely applied to materials discovery applications as machine learning methods. There are ongoing challenges in applying different optimization algorithms to discover materials with single- or multi-elemental compositions and how these algorithms differ in mining the ideal materials. We comprehensively compare 11 different optimization algorithms for the design of single- and multi-elemental crystals with targeted properties. By maximizing the bulk modulus and minimizing the Fermi energy through perturbing the parameterized elemental composition representations, we estimated the unique counts of elemental compositions, mean density scan of the objectives space, mean objectives, and frequency distributed over the materials' representations and objectives. We found that nature-inspired algorithms contain more uncertainties in the defined elemental composition design tasks, which correspond to their dependency on multiple hyperparameters. Runge-Kutta optimization (RUN) exhibits higher mean objectives, whereas Bayesian optimization (BO) displayed low mean objectives compared with other methods. Combined with materials count and density scan, we propose that BO strives to approximate a more accurate surrogate of the design space by sampling more elemental compositions and hence have lower mean objectives, yet RUN will repeatedly sample the targeted elemental compositions with higher objective values. Our work sheds light on the automated digital design of materials with single- and multi-elemental compositions and is expected to elicit future studies on materials optimization, such as composite and alloy design based on specific desired properties.