E(n)-Equivariant cartesian tensor message passing interatomic potential

Machine learning potential (MLP) has been a popular topic in recent years for its capability to replace expensive first-principles calculations in some large systems. Meanwhile, message passing networks have gained significant attention due to their remarkable accuracy, and a wave of message passing networks based on Cartesian coordinates has emerged. However, the information of the node in these models is usually limited to scalars, and vectors. In this work, we propose High-order Tensor message Passing interatomic Potential (HotPP), an E(n) equivariant message passing neural network that extends the node embedding and message to an arbitrary order tensor. By performing some basic equivariant operations, high order tensors can be coupled very simply and thus the model can make direct predictions of high-order tensors such as dipole moments and polarizabilities without any modifications. The tests in several datasets show that HotPP not only achieves high accuracy in predicting target properties, but also successfully performs tasks such as calculating phonon spectra, infrared spectra, and Raman spectra, demonstrating its potential as a tool for future research.