Resolving the body-order paradox of machine learning interatomic potentials

In many cases, the predictions of machine learning interatomic potentials (MLIPs) can be interpreted as a sum of body-ordered contributions, which is explicit when the model is directly built on neighbor density correlation descriptors and is implicit when the model captures the correlations through the non-linear functions of low body-order terms. In both cases, the "effective body-orderedness" of MLIPs remains largely unexplained: how do the models decompose the total energy into body-ordered contributions, and how does their body-orderedness affect the accuracy and learning behavior? In answering these questions, we first discuss the complexities in imposing the many-body expansion on ab initio calculations at the atomic limit. Next, we train a curated set of MLIPs on datasets of hydrogen clusters and reveal the inherent tendency of the ML models to deduce their own, effective body-order trends, which are dependent on the model type and dataset makeup. Finally, we present different trends in the convergence of the body-orders and generalizability of the models, providing useful insights into the development of future MLIPs.