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Machine learning of multi-dimensional potential energy surfaces, from purelyab initio datasets, has seen substantial progress in the past years. Gaussianprocesses, a popular regression method, have been very successful at producingrealistic potential energy surfaces from sparse datasets allowing to reduce thecomputational cost of highly accurate models. However, there are many choicesone has to take in the design of the kernel and the feature space which cansubstantially change the performance and the characteristic of the model. Inthis study we explore different Gaussian processes set ups and, morespecifically, how the permutational invariance of the target surface iscontrolled through the feature space selection.

Global descriptors of a water molecule for machine learning of potential energy surfaces