Quality-Controlled Active Learning via Gaussian Processes for Robust Structure-Property Learning in Autonomous Microscopy

Technical Summary: Quality-Controlled Active Learning via Gaussian Processes for Robust Structure–Property Learning in Autonomous Microscopy

Problem Statement
Autonomous experimental systems in materials research aim to accelerate discovery through closed-loop cycles combining physical instrumentation and machine learning (ML). However, their efficacy is frequently compromised by low-quality, noisy data. This issue is particularly acute in structure–property learning tasks, such as Image-to-Spectrum (Im2Spec) and Spectrum-to-Image (Spec2Im) translations, where inputs and labels can suffer from spatially localized degradation due to instrument drift, tip wear, or environmental instability.

Standard active learning (AL) strategies, which typically rely on uncertainty estimation (e.g., via Gaussian Processes) to select informative samples, often fail in these noisy environments. They tend to misinterpret low-fidelity, noisy measurements as highly uncertain and therefore highly informative. Consequently, these strategies prioritize the acquisition of poor-quality data, which misleads the learning model, degrades performance, and leads to inefficient sampling. While prior work has explored curiosity-driven sampling and multitask learning, these approaches often lack a mechanism to explicitly filter out data that violates physical constraints or exhibits low signal-to-noise ratios.

Methodology: ActiveQC Framework
The authors propose ActiveQC (Active Learning with Quality Control), a gated active learning framework designed to integrate curiosity-driven acquisition with a physics-informed quality control filter. The methodology operates as follows:

1. Physics-Informed Quality Metric: The system utilizes the Simple Harmonic Oscillator (SHO) model to evaluate the fidelity of Band Excitation Piezoresponse Spectroscopy (BEPS) spectra. For each candidate spectrum, the SHO model is fitted to all DC bias points. A quality score is computed as the mean coefficient of determination ($R^2$) across these frequency-domain fits. This score quantifies how well the measured response conforms to expected physical dynamics.
2. Surrogate Quality Modeling: A Gaussian Process (GP) is trained to regress these $R^2$ quality scores across the spatial domain of the sample. This GP predicts the spectral fidelity for unobserved locations, creating a spatial map of data quality.
3. Gated Acquisition Strategy: The acquisition process employs a "gating" mechanism. Before a sample is selected based on standard AL criteria, its predicted quality score ($q_i$) from the GP is checked against a predefined threshold ($\tau$).
   • If $q_i < \tau$, the sample is excluded (gated out), regardless of its uncertainty or representativeness.
   • If $q_i \geq \tau$, the sample proceeds to the scoring phase.
4. Acquisition Scoring: For samples that pass the quality gate, a unified acquisition score ($s_i$) is calculated by combining three factors:
   • Predicted Error: Estimated by a surrogate model (trained on latent features) to capture the base model's expected error (curiosity/uncertainty).
   • Distance: Euclidean distance in the latent space to the current training set (exploration of underrepresented regions).
   • Representativeness: Cosine similarity to the remaining unseen pool (coverage of the distribution).
   • The final score is a weighted sum: $s_i = \alpha \cdot \hat{e}_i + \beta \cdot d_i + \gamma \cdot r_i$.

Key Contributions

• Integration of Physics and ML: The paper introduces a framework that couples data-driven curiosity with physics-informed quality assessment, ensuring that active learning decisions are not only information-rich but also physically valid.
• Robustness to Localized Noise: By explicitly filtering out low-fidelity spectra via SHO-based $R^2$ gating, the method prevents the acquisition of corrupted data that would otherwise degrade model performance.
• Bidirectional Validation: The approach is validated on two reciprocal tasks: Im2Spec (predicting spectra from AFM images) and Spec2Im (reconstructing images from spectra), demonstrating efficacy in both forward and inverse mapping scenarios.
• Real-Time Deployment: The framework was successfully deployed in real-time on an atomic force microscope (AFM) system, demonstrating its applicability in live autonomous experiments.

Results
The authors evaluated ActiveQC against Random Sampling, Standard Active Learning (curiosity-driven), and a Multitask Learning baseline (ActiveMT) using a pre-acquired dataset of PbTiO3 thin films with artificially induced spatially localized noise.

• Im2Spec Task: ActiveQC consistently outperformed all baselines. While standard Active and ActiveMT strategies progressively selected more noisy samples (interpreting them as high-uncertainty regions), ActiveQC rapidly learned to avoid the noisy quadrant. This resulted in significantly lower Mean Squared Error (MSE) in the final acquisition rounds. Statistical analysis (Welch's t-test, $p < 0.05$) confirmed the superiority of ActiveQC.
• Spec2Im Task: Similar trends were observed. ActiveQC maintained the lowest error throughout the exploration steps, particularly in later rounds where noisy samples became more prevalent. The multitask baseline showed some improvement over standard active learning but failed to match the robustness of the gating mechanism.
• Real-Time AFM Experiments: Deployed on BiFeO3 thin films, the framework demonstrated the ability to adaptively distribute measurements. The quality gating successfully suppressed acquisitions in regions predicted to have low spectral fidelity. Analysis of the retained samples showed that high-quality subsets exhibited stronger electromechanical responses (larger loop areas and sensitivity) compared to low-quality subsets, validating the physical relevance of the filter.

Significance and Claims
The paper claims that the proposed work supports a shift toward "hybrid autonomy" in self-driving labs. The authors argue that relying solely on algorithmic uncertainty reduction is insufficient in noisy experimental environments. Instead, combining physics-informed quality assessment with active decision-making is essential for reliable discovery.

The significance lies in the demonstration that:

1. Quality Awareness is Critical: Ignoring data fidelity leads to the accumulation of misleading samples, whereas explicit quality gating prevents this failure mode.
2. Generalizability: While demonstrated on ferroelectric thin films and BEPS data, the principle of using physics-informed metrics to gate active learning is broadly applicable to other scientific domains where data quality is variable.
3. Practical Viability: The successful real-time deployment on an AFM platform proves that such quality-controlled loops can operate robustly under practical experimental constraints, offering a pathway to more reliable and de-risked autonomous materials research.