Data efficiency and extrapolation trends in neural network interatomic potentials

Over the last few years, key architectural advances have been proposed for neural network interatomic potentials (NNIPs), such as incorporating message-passing networks, equivariance, or many-body expansion terms. Although modern NNIP models exhibit nearly negligible differences in energy/forces errors, improvements in accuracy are still considered the main target when developing new NNIP architectures. In this work, we investigate how architectural choices influence the trainability and generalization error in NNIPs, revealing trends in extrapolation, data efficiency, and loss landscapes. First, we show that modern NNIP architectures recover the underlying potential energy surface (PES) of the training data even when trained to corrupted labels. Second, generalization metrics such as errors on high-temperature samples from the 3BPA dataset are demonstrated to follow a scaling relation for a variety of models. Thus, improvements in accuracy metrics may not bring independent information on the robust generalization of NNIPs. To circumvent this problem, we relate loss landscapes to model generalization across datasets. Using this probe, we explain why NNIPs with similar accuracy metrics exhibit different abilities to extrapolate and how training to forces improves the optimization landscape of a model. As an example, we show that MACE can predict PESes with reasonable error after being trained to as few as five data points, making it an example of a "few-shot" model for learning PESes. On the other hand, models with similar accuracy metrics such as NequIP show smaller ability to extrapolate in this extremely low-data regime. Our work provides a deep learning justification for the performance of many common NNIPs, and introduces tools beyond accuracy metrics that can be used to inform the development of next-generation models.