The ability of machine learning models to predict energy calculations, or energy corrections between two levels of theory, has been demonstrated for a number of systems in the literature. A key component of this is the representation or descriptor of the system, of which there are now many. Comparisons between descriptors are lacking, and are typically carried out by using different descriptors for a given model and observing the outcome. It would be useful to have an approach to comparing descriptors that is independent of the machine learning model used. Current rules of thumb for a good descriptor include that the descriptor must be invariant to permutation, unique, and preferably small to reduce the effects of the curse dimensionality. The first of these can generally be shown a priori, but measuring the latter two can be difficult in practice.<br/><br/>Here we describe a simple metric for quantifying the effectiveness of a given descriptor, in terms of its uniqueness, local constancy, and dimensionality, allowing for the best descriptor for a given dataset to be identified. Any hyperparameters of a descriptor can also then be optimised for these conditions, before any machine learning takes place. We demonstrate this in the field of crystal structure prediction, where thousands of lattice energy calculations at a high level of theory are often required. By systematically identifying the best descriptor and then selecting a training set that best represents the space, we find sub kJ/mol prediction errors in correcting force field lattice energies to density functional theory with a range of machine learning models, using training set fractions as low as 10%.

Systematically identifying the best chemical representation for machine learning with applications in crystal structure prediction

255th National Meeting (2018)

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