Smart sampling for optimized materials: A Gaussian process framework for region-of-interest active learning

Discovering materials with properties that meet user-defined performances remains a critical yet resource-intensive challenge in materials engineering, often requiring costly experiments or simulations. This paper introduces a data-efficient Gaussian Process (GP) active learning framework designed to map multidimensional design spaces and efficiently identify subsets of the output space that represent the optimal or acceptable range for a specific application, defined as Regions of Interest (RoIs). Three novel acquisition function families were proposed: (i) Probability-Entropy acquisitions, balancing exploration and exploitation without additional tuning; (ii) Dual Level-Set Gaussian Bound, extending classical straddle heuristics to multiple thresholds; and (iii) Expected Mahalanobis (ExM), generalizing boundary-focused sampling to arbitrary multivariate target distributions. Benchmark evaluations on synthetic functions and a Al/CuO thermite powder mixture design case demonstrate that the ExM acquisition significantly outperforms existing methods, achieving faster RoI discovery, lower uncertainty, and more complete mapping with minimal iterations. We found that ExM removes the need to tune an explicit exploration parameter. It only requires choosing a target distribution within the RoI, for which we provide simple default options (Uniform or truncated Normal) along with practical guidelines. Applied to Al/CuO thermite formulation for welding applications, ExM efficiently identifies diverse optimized compositions within the target RoI, minimizing redundancy and experimental cost. Overall, ExM provides a scalable and flexible RoI-targeted active learning approach that removes exploration-weight tuning for materials design and beyond.