# Bayesian Active Learning for Scanning Probe Microscopy: from Gaussian Processes to Hypothesis Learning

arXiv: https://arxiv.org/abs/2205.15458 · HTML: https://mlsanity.com/paper/2205.15458/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 115 references that are in the map.
- First posted on arXiv 30 May 2022.

## Builds on (most cited first, 14 of 14)

- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Barlow Twins: Self-Supervised Learning via Redundancy Reduction](https://mlsanity.com/paper/2103.03230/) (2021)
- [Concrete Problems in AI Safety](https://mlsanity.com/paper/1606.06565/) (2016)
- [In Search of Lost Domain Generalization](https://mlsanity.com/paper/2007.01434/) (2020)
- [Deep Neural Networks are Easily Fooled: High Confidence Predictions for Unrecognizable Images](https://mlsanity.com/paper/1412.1897/) (2014)
- [A Tutorial on Bayesian Optimization](https://mlsanity.com/paper/1807.02811/) (2018)
- [Recognition in Terra Incognita](https://mlsanity.com/paper/1807.04975/) (2018)
- [Pyro: Deep Universal Probabilistic Programming](https://mlsanity.com/paper/1810.09538/) (2018)
- [Composable Effects for Flexible and Accelerated Probabilistic Programming in NumPyro](https://mlsanity.com/paper/1912.11554/) (2019)
- [Understanding the Failure Modes of Out-of-Distribution Generalization](https://mlsanity.com/paper/2010.15775/) (2020)
- [Understanding predictive information criteria for Bayesian models](https://mlsanity.com/paper/1307.5928/) (2013)
- [Using stacking to average Bayesian predictive distributions](https://mlsanity.com/paper/1704.02030/) (2017)
- [Compressed Sensing of Scanning Transmission Electron Microscopy (STEM) on Non-Rectangular Scans](https://mlsanity.com/paper/1805.04957/) (2018)

## Built on by (most cited first, 16 of 16)

- [Deep Kernel Methods Learn Better: From Cards to Process Optimization](https://mlsanity.com/paper/2303.14554/) (2023)
- [Discovery of structure-property relations for molecules via hypothesis-driven active learning over the chemical space](https://mlsanity.com/paper/2301.02665/) (2023)
- [Unraveling the Impact of Initial Choices and In-Loop Interventions on Learning Dynamics in Autonomous Scanning Probe Microscopy](https://mlsanity.com/paper/2402.00071/) (2024)
- [Bayesian Co-navigation: Dynamic Designing of the Materials Digital Twins via Active Learning](https://mlsanity.com/paper/2404.12899/) (2024)
- [Co-orchestration of Multiple Instruments to Uncover Structure-Property Relationships in Combinatorial Libraries](https://mlsanity.com/paper/2402.02198/) (2024)
- [Beyond Optimization: Exploring Novelty Discovery in Autonomous Experiments](https://mlsanity.com/paper/2508.20254/) (2025)
- [Measurements with Noise: Bayesian Optimization for Co-optimizing Noise and Property Discovery in Automated Experiments](https://mlsanity.com/paper/2410.02717/) (2024)
- [X-Factor: Quality Is a Dataset-Intrinsic Property](https://mlsanity.com/paper/2505.22813/) (2025)
- [Predicting Battery Capacity Fade Using Probabilistic Machine Learning Models With and Without Pre-Trained Priors](https://mlsanity.com/paper/2410.06422/) (2024)
- [Human-AI Synergy in Adaptive Active Learning for Continuous Lithium Carbonate Crystallization Optimization](https://mlsanity.com/paper/2507.19316/) (2025)
- [DIVIDE: A Framework for Learning from Independent Multi-Mechanism Data Using Deep Encoders and Gaussian Processes](https://mlsanity.com/paper/2511.12745/) (2025)
- [Novelty-Driven Target-Space Discovery in Automated Electron and Scanning Probe Microscopy](https://mlsanity.com/paper/2603.16715/) (2026)
- [Quality-Controlled Active Learning via Gaussian Processes for Robust Structure-Property Learning in Autonomous Microscopy](https://mlsanity.com/paper/2603.29135/) (2026)
- [PATHFINDER: Multi-objective discovery in structural and spectral spaces](https://mlsanity.com/paper/2604.04194/) (2026)
- [Beyond Scalar Objectives: Expert-Feedback-Driven Autonomous Experimentation for Scientific Discovery at the Nanoscale](https://mlsanity.com/paper/2605.21820/) (2026)
- [STEMGym: Benchmarking Sequential Decision-Making under Dose Budgets in Autonomous Electron Microscopy](https://mlsanity.com/paper/2606.29592/) (2026)

## Abstract (arXiv)

Recent progress in machine learning methods, and the emerging availability of programmable interfaces for scanning probe microscopes (SPMs), have propelled automated and autonomous microscopies to the forefront of attention of the scientific community. However, enabling automated microscopy requires the development of task-specific machine learning methods, understanding the interplay between physics discovery and machine learning, and fully defined discovery workflows. This, in turn, requires balancing the physical intuition and prior knowledge of the domain scientist with rewards that define experimental goals and machine learning algorithms that can translate these to specific experimental protocols. Here, we discuss the basic principles of Bayesian active learning and illustrate its applications for SPM. We progress from the Gaussian Process as a simple data-driven method and Bayesian inference for physical models as an extension of physics-based functional fits to more complex deep kernel learning methods, structured Gaussian Processes, and hypothesis learning. These frameworks allow for the use of prior data, the discovery of specific functionalities as encoded in spectral data, and exploration of physical laws manifesting during the experiment. The discussed framework can be universally applied to all techniques combining imaging and spectroscopy, SPM methods, nanoindentation, electron microscopy and spectroscopy, and chemical imaging methods, and can be particularly impactful for destructive or irreversible measurements.