Gaussian processes occupy a distinctive position in scientific machine learning: they make predictions with calibrated uncertainties, incorporate prior physical knowledge through kernel design, and degrade gracefully when data are scarce — properties of particular value in the physical sciences where measurements are expensive and datasets are small. This workshop develops Gaussian process regression from first principles, covering kernel functions, hyperparameter optimisation, and predictive distributions, with emphasis on what uncertainty quantification means in practice and why scientists should care about it.

The session then examines Bayesian optimisation — the methodology that uses GP-based surrogate models to guide sequential experimental or computational searches toward optimal conditions with minimal evaluations. Acquisition functions (expected improvement, upper confidence bound, entropy search) and the exploration– exploitation trade-off are developed with examples from materials science and electrochemistry. The closely related methodology of active learning, in which uncertainty estimates are used to decide which experiments or calculations to prioritise next, is examined in the context of both high-throughput computation and laboratory experimentation.

The workshop also addresses the GAP/SOAP framework, in which Gaussian process regression underpins the construction of interatomic potentials with systematically improvable accuracy, providing a bridge to the ML force field methods covered in Workshop 6.

Extended Key Takeaways & Outputs

• Working knowledge of GP regression, kernel design, and uncertainty quantification

• Practical understanding of Bayesian optimisation and active learning for experimental design

• Insight into acquisition functions and the exploration–exploitation trade-off

• Connection to interatomic potential construction via the GAP/SOAP framework

• Foundation for the autonomous experimentation methods addressed in Workshop 13