Leveraging feature gradient for efficient acquisition function maximization in material composition design

Abstract

Bayesian optimization (BO) has been widely employed for alloy composition design, but faces unique challenges in this domain when maximizing the acquisition function (AF), which is a critical step for selecting the best candidate. While various optimization methods exist for maximizing AF, material composition design presents difficulties that include the need to translate compositions into material features, rapid polynomially expanding design spaces as component numbers increase, and compositional constraints (e.g., sum to 100%). To address this issue, we propose a strategy that leverages numerical feature gradient for efficient AF maximization in material composition design. By establishing a differentiable pipeline from alloy compositions, through material features and model predictions, to AF values, our strategy enables efficient navigation from initial compositional guesses to optimal solutions. This approach reduces the complexity of the inner optimization problem from rapid polynomial (i.e., in the case of full enumeration) to empirically observed linear scale with respect to the number of components, making it efficient for medium-scaled design spaces (up to 10 components) while showing potential for scaling to larger compositional spaces. Additionally, initiating the process with randomly generated compositions promotes more diverse solutions, as evidenced by a slower decay of compositional state entropy compared to traditional enumeration-based approaches. Furthermore, the flexibility of our method allows for tailoring the optimization process by adjusting key settings, such as the number of initial compositions, the choice of AFs, surrogate models, and the formulas used to calculate material features. We envision this strategy as a scalable and modular methodology for advancing materials design, particularly in the composition design of high-entropy alloys, ceramics, and perovskites, where elemental compositions can be adjusted as continuous variables.