Gaussian Process Regression
Gaussian process regression treats an unknown function as a distribution over functions in which any finite set of values is jointly normal, with correlations set by a kernel. Conditioning on data gives a predictive mean and variance at new points, which makes GPs a common choice for surrogate models, Bayesian optimization and interatomic potentials where calibrated uncertainty is needed. See also Uncertainty quantification and Bayesian inference.
Joint Gaussian process over a function and its derivatives (2022)
Zhan and Kitchin built a GP whose covariance spans the function and its first and second derivatives, using derivatives of an RBF kernel computed with automatic differentiation, so that properties defined by derivatives (the equilibrium volume from a zero slope and the bulk modulus from the curvature of an energy-volume curve) can be sampled consistently from one posterior (Zhan 2022). Applied to DFT data for Pd and Au, the GP posteriors were wider than regression-based intervals and covered the predictions of almost all analytical equations of state, while variance grew with derivative order and toward the data edges. Summary: zhan2022a.