PATHFINDER: Multi-objective discovery in structural and spectral spaces

Abstract: Automated decision-making is becoming key for automated characterization including electron and scanning probe microscopies and nano indentation. Most machine learning driven workflows optimize a single predefined objective and tend to converge prematurely on familiar responses, overlooking rare but scientifically important states. More broadly, the challenge is not only where to measure next, but how to coordinate exploration across structural, spectral, and measurement spaces under finite experimental budgets while balancing target-driven optimization with novelty discovery. Here we introduce PATHFINDER, a framework for autonomous microscopy that combines novelty driven exploration with optimization, helping the system discover more diverse and useful representations across structural, spectral, and measurement spaces. By combining latent space representations of local structure, surrogate modeling of functional response, and Pareto-based acquisition, the framework selects measurements that balance novelty discovery in feature and object space and are informative and experimentally actionable. Benchmarked on pre acquired STEM EELS data and realized experimentally in scanning probe microscopy of ferroelectric materials, this approach expands the accessible structure property landscape and avoids collapse onto a single apparent optimum. These results point to a new mode of autonomous microscopy that is not only optimization-driven, but also discovery-oriented, broad in its search, and responsive to human guidance.

• The paper introduces the PATHFINDER framework that balances structural novelty and spectral optimization using a Pareto-based, multi-objective Bayesian approach.
• It employs a dual-branch method by integrating a variational autoencoder for latent structural mapping with a deep-kernel Gaussian process surrogate for online functional prediction.
• Experimental results on STEM-EELS and SPM demonstrate that PATHFINDER significantly enhances the discovery of rare, functionally salient material states under limited measurement budgets.

Multi-Objective Discovery in Autonomous Microscopy: The PATHFINDER Framework

Introduction

The problem of efficient, autonomous exploration in high-dimensional experimental domains—exemplified by scanning probe and electron microscopies—remains a central challenge in automated materials characterization. Traditional ML-based autonomous experimentation architectures are dominated by single-objective strategies that prioritize acceleration towards a scalarized, operator-defined target, typically resulting in suboptimal manifold coverage and neglect of rare yet scientifically salient states. The PATHFINDER framework, introduced in "PATHFINDER: Multi-objective discovery in structural and spectral spaces" (2604.04194), generalizes active experimental design via a fundamentally multi-objective approach, balancing structural novelty with functional (spectral or measurement-driven) optimization. This enables richer navigation of the coupled structure-property landscape, with the explicit goal of maximizing both scientific discovery and actionable, experiment-driven utility under stringent resource constraints.

PATHFINDER Architecture and Methodology

PATHFINDER unifies two core branches within a closed-loop, multi-objective Bayesian optimization framework:

1. Structural Novelty Quantification (R1): Input structural data (e.g., HAADF or AFM images) are decomposed into local patches and embedded in a learned latent space via a VAE. Distance metrics in this latent space, such as neighborhood-based or global-mean-referenced dissimilarity, serve as adaptive measures of structural novelty. This approach sharply contrasts with exhaustively sampled or fixed-policy strategies by directly prioritizing underexplored regions in the high-dimensional image manifold.
2. Functional Optimization (R2): The spectral/functional branch models the structure-property mapping using a deep-kernel GP surrogate, trained online as new measurements accrue. For each candidate location, the scalarized functional reward (e.g., EELS intensity in a target energy window or SPM-derived nonlinear coefficients) estimates the scientific utility or material performance as a function of its structural context.

These two branches are combined via Pareto-based acquisition (expected hypervolume improvement, EHVI) to select measurement coordinates that optimally traverse the trade-off between exploring structurally distinct states and exploiting regions with favorable functional responses. Measurement scheduling is thus inherently budget-aware and path-dependent, with the capacity for human-in-the-loop interventions via dynamic reward, acquisition policy, or scalarizer updates.

Experimental Validation

Two distinct experimental contexts substantiate PATHFINDER's efficacy:

1. Benchmarking with STEM-EELS Nanoparticle Data

On a fully pre-acquired dataset of fluorine- and tin-co-doped indium oxide nanoparticle assemblies, PATHFINDER demonstrates sample-efficient discovery across ~8,000 candidate image patches. The framework simultaneously populates the joint Pareto front of rare structural motifs (measured in VAE latent space) and energetically salient EELS responses. Instead of premature convergence onto a single high-reward region, acquisitions cover a broad manifold span, ensuring that weakly represented yet functionally interesting states are interrogated. This approach increases experimental informativeness per measurement, crucial in resource-limited or fragile systems.

2. On-the-Fly SPM of Ferroelectric Thin Films

In autonomous SPM on strained PbTiO$_3$/KTaO$_3$ heterostructures, PATHFINDER is initialized from a single structural scan, adaptively guiding subsequent spectroscopic force probe measurements. Here, the trajectory of measurements dynamically tracks both evolving structural rarity (referenced to previously sampled points) and updated functional surrogates. The algorithm actively redirects the experimental path toward novel domain boundaries or interfaces exhibiting nontrivial electromechanical responses, accomplishing broader latent manifold coverage than static, non-adaptive policies.

Strong Numerical Findings and Distinct Claims

• The adaptive novelty formulation yields a systematically larger fraction of the latent structural space explored for a fixed experimental budget compared to static (global-referenced) novelty metrics.
• Acquisitions selected via EHVI in the (R1, R2) space robustly avoid rapid collapse to single-objective optima—sampling is distributed across structurally and functionally diverse regions.
• The search trajectories produced by PATHFINDER exhibit characteristic alternation between local exploitation (refinement around a promising region) and global exploration (relocation to novel latent space basins), as manifested by nonmonotonic but locally increasing reward trends and larger latent-space displacements between measurements.
• There is clear evidence that high structural novelty and maximal functional response are only partially correlated, necessitating explicit multi-objective control to avoid suboptimal measurement allocation.

Theoretical and Practical Implications

PATHFINDER provides a formalism for recasting autonomous experimental orchestration beyond single-scalar optimization, especially in regimes where structural diversity is equally or more valuable than scalar performance metrics. By treating both the novelty and functional objectives as first-class, dynamically updated rewards, the framework generalizes to multimodal, sequential, and non-differentiable measurement landscapes. The path-dependence induced by adaptive novelty prioritization enables principled control over manifold coverage, reducing brittleness and mitigating convergence on spurious or operator-biased optima.

Practically, PATHFINDER is directly extensible to:

• Joint multimodal imaging/spectroscopy where acquisition costs and instrument constraints differ across modalities.
• Materials discovery pipelines where rare microstructural states are of outsized importance (e.g., defect-driven properties, inhomogeneous functional domains).
• Closed-loop experiment settings requiring real-time human guidance or hypothesis switching.

Future Directions

Immediate developments for PATHFINDER include extension to multi-fidelity and genuinely multimodal reward landscapes, integration of external priors or theory-derived constraints, and more sophisticated human-in-the-loop paradigms. Algorithmic advances in surrogate learning, acquisition function design, and cost-aware experiment scheduling will further enhance the framework’s applicability, particularly in resource-intensive scientific instruments and combinatorial discovery settings.

Conclusion

The PATHFINDER framework establishes a robust paradigm for multi-objective, novelty-aware autonomous experimentation in microscopy and beyond. By unifying latent-space structural exploration with surrogate functional optimization through Bayesian multi-objective design and adaptive acquisition, it advances the efficiency and scientific yield of autonomous discoveries in complex material systems. This framework paves the way for more broadly generalizable, physically-grounded, and hypothesis-responsive AI-orchestrated experimental science.