The set of kernel hyperparameters is {σ 2 , l, σ 2 n }, which controls the variance, lengthscale and noise of the kernel, respectively, and they are determined by maximum likelihood estimation (MLE). This differs from the majority of works done on the GPR learning of energy surfaces, which does not explicitly account for noise inherent to the method but rather employs a regularization term. Although a simple difference, it has strong consequences on the MECI optimizations as we will discuss subsequently. An important point of note here is, although we are modelling and fitting the local energetic variation as i.i.d. Gaussian noise, they are in fact more appropriately considered as deterministic noise. For example, multiple random samples of the energy at the same structure yields a delta distribution, and averaging over a large sample does not cancel out the noise. Regardless, this model provides a convenient formalism for handling the local energetic variations and learning a smooth surface. Another assumption made here is that the local energetic variations within a set of closely distanced structures are small compared to the total energetic variations across the surface of interest. That is, for the range of local energetic variations L and the range of energies over the nuclear geometries of interest G, L ≪ G. This is to ensure that the learned surrogate is not dominated by noise and is interpretable.