ICDP: an irreducible Cartesian dynamic-attention potential for atomistic simulations

Abstract

Machine learning interatomic potentials (MLIPs) combine the computational efficiency of conventional empirical potentials with the predictive accuracy of first-principles methods and have substantially advanced materials science and atomistic simulation. Although Cartesian-coordinate representations of atomic environments offer conceptual simplicity and geometric intuitiveness, conventional reducible Cartesian tensors mix components of different rotational orders and contain redundant trace components. Moreover, the number of components increases as 3 ℓ with tensor rank, potentially increasing the complexity of high-order geometric representations and feature coupling. To address these limitations, we propose the Irreducible Cartesian Dynamic-Attention Potential (ICDP). Through irreducible Cartesian tensor decomposition, ICDP projects dense Cartesian tensor products of edge directions onto compact irreducible subspaces of dimension 2 ℓ + 1 , thereby reducing representational redundancy while preserving rotational equivariance. It further introduces a dynamic attention mechanism consisting of a scalar environment branch and an irreducible geometry branch, enabling the model to adaptively modulate the contributions of different neighbours according to the local atomic environment. ICDP achieves high accuracy in energy and force prediction on the bulk water, LiPS, and GAP17 datasets. Molecular dynamics simulations further demonstrate its ability to describe the structural and dynamical properties of diverse systems. Our code is publicly available at https://github.com/lixuan000/ICDP