A Novel Constrained Sampling Method for Efficient Exploration in Materials and Chemical Mixture Design

Abstract: Efficient exploration of multicomponent material composition spaces is often limited by time and financial constraints, particularly when mixture and synthesis constraints exist. Traditional methods like Latin hypercube sampling (LHS) struggle with constrained problems especially in high dimensions, while emerging approaches like Bayesian optimization (BO) face challenges in early-stage exploration. This article introduces ConstrAined Sequential laTin hypeRcube sampling methOd (CASTRO), an open-source tool designed to address these challenges. CASTRO is optimized for uniform sampling in constrained small- to moderate-dimensional spaces, with scalability to higher dimensions through future adaptations. CASTRO uses a divide-and-conquer strategy to decompose problems into parallel subproblems, improving efficiency and scalability. It effectively handles equality-mixture constraints, ensuring comprehensive design space coverage and leveraging LHS and LHS with multidimensional uniformity (LHSMDU). It also integrates prior experimental knowledge, making it well-suited for efficient exploration within limited budgets. Validation through two material design case studies, a four-dimensional problem with near-uniform distributions and a nine-dimensional problem with additional synthesis constraints, demonstrates CASTRO's effectiveness in exploring constrained design spaces for materials science, pharmaceuticals and chemicals. The software and case studies are available on GitHub.