Cost-aware Bayesian optimization of real-world nanoindentation workflows for accelerated mechanical characterization

Abstract

Accelerating the discovery of mechanical properties in combinatorial materials requires autonomous experimentation that accounts for both instrument behavior and experimental cost. Here, an automated nanoindentation (AE-NI) framework is developed and validated for adaptive mechanical mapping of combinatorial thin-film libraries. The method integrates heteroskedastic Gaussian-process modeling with cost-aware Bayesian optimization to dynamically select indentation locations and hold times, minimizing total testing time while preserving measurement accuracy. A detailed emulator and cost model capture the intrinsic penalties associated with lateral motion, drift stabilization, and reconfiguration-factors often neglected in conventional active-learning approaches. To prevent kernel-length-scale collapse caused by disparate time scales, a hierarchical meta-testing workflow combining local grid and global exploration is introduced. Implementation of the workflow is shown on an experimental Ta–Ti–Hf–Zr thin-film library. The proposed framework achieves nearly a thirty-fold improvement in property-mapping efficiency relative to grid-based indentation, demonstrating that incorporating cost and drift models into probabilistic planning substantially improves performance. This study establishes a generalizable strategy for optimizing experimental workflows in autonomous materials characterization and can be extended to other high-precision, drift-limited instruments.