gaussian-process-materials

Gaussian Process Materials Models

Description

This skill covers Gaussian process regression (GPR) for materials and chemistry datasets: descriptor selection, feature scaling, kernel design, small-data modeling, calibrated uncertainty, heteroscedastic noise, cross-validation, multi-output and multi-fidelity extensions, and integration with Bayesian optimization and active learning. Invoke this skill when building a data-efficient surrogate model for DFT, experimental, or database-derived properties where uncertainty estimates and query decisions matter as much as point predictions.

Domain Context

Gaussian processes are probabilistic nonparametric models. A GP defines a distribution over functions; after observing data, it returns both a posterior mean and a posterior variance for each new input. This makes GPs attractive in computational materials science, where datasets are often small because DFT or experiment is expensive, and where the next calculation should be chosen by expected information gain or improvement rather than by random search.

The GP is only as meaningful as the representation and kernel. A crystal composition encoded by Magpie features, a SOAP vector, a graph kernel, and a hand-picked descriptor set each define a different notion of similarity. The kernel then states how property covariance decays with that similarity. A smooth RBF kernel assumes nearby descriptor vectors have smoothly varying properties; a Matern kernel permits rougher functions; additive kernels assume separable contributions from feature groups; product kernels encode interactions. These are scientific assumptions, not just hyperparameters.

GP uncertainty is epistemic under the model, not physical uncertainty by default. Posterior standard deviation grows far from the training data only if the kernel and feature scaling recognize that distance. In high-dimensional descriptor spaces, distances can concentrate, kernels can become nearly constant, and the GP can become overconfident or numerically unstable. Calibration against held-out data is required before using posterior uncertainty as an acquisition signal.