Improving Machine Learning Modelling of Physical Properties with Isometry Invariants*

Machine learning techniques are increasingly capable of improving the accuracy of atomistic simulations. However, many challenges remain before we can build practical, robust, and fully transferable models. One of these challenges is the problem of quantifying the similarity between any two given structures. A promising route to addressing this problem are the recently developed isometry invariants for (periodic) point clouds, which are complete and Lipschitz continuous. We show that the efficient calculation of structural and compositional invariants across large inorganic materials datasets can improve data handling and model training in machine learning tasks, specifically to better understand, quantify, and impute the data. We also discuss how invariants-based distances can be used to optimize the selection of representative structures and perform a quantifiable exploration of phase transitions and predicted properties in terms of perturbations such as adding strain or changing the amount of disorder.