Beyond Scalar Objectives: Expert-Feedback-Driven Autonomous Experimentation for Scientific Discovery at the Nanoscale.

Self-driving laboratories or autonomous experimentation are emerging as transformative platforms for accelerating scientific discovery. Bayesian optimization (BO) is among the most widely used machine learning frameworks in self-driving laboratories, but these BO-based frameworks rely on predefined scalar descriptors to guide experimentation. This limits their ability to handle complex phenomena that are difficult to formalize as scalar descriptors. In many situations, the determination of an appropriate scalar descriptor can be challenging, and may fail to capture subtle yet scientifically important phenomena apparent to experts with interdisciplinary insight. This problem is particularly pronounced in nanoscale imaging experiments, where strong local heterogeneity, multidimensional observations, and emergent physical behaviors often cannot be effectively represented using scalar metrics. To overcome this limitation, here we develop deep-kernel pairwise learning (DKPL), an approach for autonomous microscopy experiments which incorporates human expertise and interdisciplinary scientific knowledge into an active learning loop. Instead of relying on explicit scalar objectives, DKPL enables experts to directly evaluate which experimental output is more promising using interdisciplinary knowledge. DKPL then learns a latent utility function from these expert judgments to guide subsequent autonomous microscopy experiments. We demonstrate DKPL's performance in learning physically meaningful nanoscale structures in lead titanate thin films while effectively prioritizing high-information measurement regions using an experimental model dataset with known ground truth. We further apply DKPL to analyze the character of ferroelectric domain walls, where we find DKPL capable of distinguishing between high and low characteristic domain-wall angles in lead zirconium titanate, and able to discover both head-to-head and tail-to-tail domain-wall character in erbium manganite. Autonomous experiments in mixed-phase bismuth ferrite also demonstrate DKPL's ability to link material structure with their properties in on-the-fly measurements. This development demonstrates an approach to integrate expert knowledge into autonomous microscopy experiments across a variety of material systems, and demonstrates a pathway toward expert-guided self-driving laboratories capable of addressing scientific problems beyond the limits of scalar-metrics-driven learning.