Machine learning force fields (MLFFs) have instigated a groundbreaking shift in molecular dynamics (MD) simulations across a wide range of fields, such as physics, chemistry, biology, and materials science. Incorporating higher order many-body interactions can enhance the expressiveness and accuracy of models. Recent models have achieved this by explicitly including up to four-body interactions. However, five-body interactions, which have relevance in various fields, are still challenging to incorporate efficiently into MLFFs. In this work, we propose the quintuple network (QuinNet), an end-to-end graph neural network that efficiently expresses many-body interactions up to five-body interactions with \emph{ab initio} accuracy. By analyzing the topology of diverse many-body interactions, we design the model architecture to efficiently and explicitly represent these interactions. We evaluate QuinNet on public datasets of small molecules, such as MD17 and its revised version, and show that it is compatible with other state-of-the-art models on these benchmarks.

Incorporating higher order cosine series into the QuinNet model is necessary in certain cases. Furthermore, the results of the 6-layer QuinNet model are presented in the table. This dataset offers valuable quantum chemical insights into the chemical space of small organic molecules and is widely acknowledged as a benchmark for calibrating, analyzing, and evaluating new methods in this area. Specifically, as shown in Fig. S2 (a), we GPU. Furthermore, detailed settings of hyperparameters are summarized in the Table S 4.

Machine learning force fields (MLFFs) have instigated a groundbreaking shift in molecular dynamics (MD) simulations across a wide range of fields, such as physics, chemistry, biology, and materials science. Incorporating higher order many-body interactions can enhance the expressiveness and accuracy of models. Recent models have achieved this by explicitly including up to four-body interactions. However, five-body interactions, which have relevance in various fields, are still challenging to incorporate efficiently into MLFFs. In this work, we propose the quintuple network (QuinNet), an end-to-end graph neural network that efficiently expresses many-body interactions up to five-body interactions with \emph{ab initio} accuracy. By analyzing the topology of diverse many-body interactions, we design the model architecture to efficiently and explicitly represent these interactions.