Exploring the robust extrapolation of high-dimensional machine learning potentials

We show that, contrary to popular assumptions, predictions from machine learning potentials built upon highdimensional atom-density representations almost exclusively occur in regions of the representation space which lie outside the convex hull defined by the training set points. We then propose a perspective to rationalize the domain of robust extrapolation and accurate prediction of atomistic machine learning potentials in terms of the probability density induced by training points in the representation space.