Low-rank matrix and tensor approximations for compression of machine-learning interatomic potentials

Journal of Chemical Physics. 2025. Vol. 163. No. 24. Article 244112.

Vorotnikov I., Romashov F., Rybin N., Rakhuba M., Novikov I.

Machine-learning interatomic potentials (MLIPs) have become a mainstay in computationally guided materials science, surpassing traditional force fields due to their flexible functional form and superior accuracy in reproducing physical properties of materials. This flexibility is achieved through mathematically rigorous basis sets that describe interatomic interactions within a local atomic environment. The number of parameters in these basis sets influences both the size of the training dataset required and the computational speed of the MLIP. Consequently, compressing MLIPs by reducing the number of parameters is a promising route to more efficient simulations. In this work, we use low-rank matrix and tensor factorizations under fixed-rank constraints to achieve this compression. In addition, we demonstrate that an algorithm with automatic rank augmentation helps to find a deeper local minimum of the fitted potential. The methodology is mainly verified using the Moment Tensor Potential (MTP) model and benchmarked on multi-component systems: a Mo–Nb–Ta–W medium-entropy alloy, molten LiF–NaF–KF, and a glycine molecular crystal. The proposed approach achieves up to 50% compression without any loss of MTP accuracy. We also demonstrate that the developed methodology is universal and can be applied to compress other MLIPs on the example of atomic cluster expansion.

Keywords: low-rank approximation, Riemannian manifold, Density functional theory (DFT), magnetic machine-learning interatomic potentials