PATHFINDER: Multi-objective discovery in structural and spectral spaces

Modern automated microscopy faces a fundamental discovery challenge: in many systems, the most important scientific information does not reside in the immediately visible image features, but in the target space of sequentially acquired spectra or functional responses, making it essential to develop strategies that can actively search for new behaviors rather than simply optimize known objectives. Here, we developed a deep-kernel-learning BEACON framework that is explicitly designed to guide discovery in the target space by learning structure-property relationships during the experiment and using that evolving model to seek diverse response regimes. We first established the method through demonstration workflows built on pre-acquired ground-truth datasets, which enabled direct benchmarking against classical acquisition strategies and allowed us to define a set of monitoring functions for comparing exploration quality, target-space coverage, and surrogate-model behavior in a transparent and reproducible manner. This benchmarking framework provides a practical basis for evaluating discovery-driven algorithms, not just optimization performance. We then operationalized and deployed the workflow on STEM, showing that the approach can transition from offline validation to real experimental implementation. To support adoption and extension by the broader community, the associated notebooks are available, allowing users to reproduce the workflows, test the benchmarks, and adapt the method to their own instruments and datasets.

Autonomous experimentation has transformed microscopy and materials discovery by enabling closed-loop optimization including imaging and spectroscopy tuning, strucutre property relationship discovery, and exploration of combinatorial libraries. However, most current workflows remain limited to selecting measurements within fixed objective or hypothesis spaces, rather than generating new physical models from experimental data. Here, we introduce an open hypothesis-learning framework that combines symbolic regression with large-language-model-based physical evaluation and implement it for autonomous scanning probe microscopy. Symbolic regression generates candidate analytical relationships directly from sparse measurements, while the language-model evaluator ranks these candidates according to physical plausibility, scaling behavior, and consistency with known mechanisms. We demonstrate the approach on autonomous piezoresponse force microscopy measurements of ferroelectric domain switching in a PZT thin film. Starting from five seed measurements, the workflow evolves from physically incomplete candidate expressions toward interpretable voltage-time growth laws consistent with kinetic domain-wall motion. This work extends autonomous microscopy from closed-loop optimization toward open hypothesis discovery, where candidate physical laws emerge from the experiment itself rather than being specified in advance. More broadly, the framework establishes a route for integrating symbolic regression, physical reasoning, and adaptive experimentation into hierarchical autonomous scientific workflows.

Scanning probe microscopy provides nanoscale access to structural, electrical, electromechanical, magnetic, and mechanical properties of materials. Its increasing use for wafer-scale characterization and combinatorial materials exploration creates a need to distribute measurements efficiently across large spatial domains. This is particularly important when available modalities differ in acquisition time and potential for tip and sample damage, making exhaustive multimodal mapping over spatial grids impractical. Here, we demonstrate multitask scanning probe microscopy, a live, closed-loop workflow in which a multitask Gaussian process learns spatial and cross-modal relationships and autonomously selects both the next measurement location and the next experimental protocol. The approach is implemented on an automated large-sample atomic force microscope and demonstrated on a composition-spread AlScN wafer using tapping-mode and Dual AC Resonance Tracking (DART) measurements. Paired initial measurements establish the relation between the tasks, after which noncoincident measurements are used to update both response landscapes. The resulting workflow extends active learning in scanning probe microscopy from spatial sampling to autonomous allocation of measurement modalities and provides a basis for combining rapid, weakly perturbative imaging with slower contact, electrical, electromechanical, magnetic, or spectroscopic measurements.