Efficient Rigorous Stress Field Calculations for Machine Learning Interatomic Potentials

The computation of atomistic stress fields plays a central role in linking atomistic simulations to continuum models. However, commonly used stress measures, such as the per-atom virial stress, do not constitute true spatial stress fields consistent with the continuum balance laws. Moreover, when constructing continuum-consistent atomistic stress fields, fundamental non-uniqueness arises from the decomposition of atomic forces into interatomic contributions. While physically motivated force decompositions are often available for conventional physics-based interatomic potentials, these approaches become problematic for modern machine-learning potentials that are formulated in terms of high-dimensional, data-driven descriptors rather than explicit interatomic distances. In this work, we develop a computationally efficient projection-based force decomposition framework that enables the construction of smooth and continuous atomistic stress fields for both conventional and machine-learning interatomic potentials. We show that the proposed method avoids reliance on distance-based chain-rule formulations and remains robust to model representation choices. Validation across a variety of interatomic potentials for diamond-cubic silicon demonstrates that the resulting stress fields exhibit significantly reduced noise. Our method establishes a consistent and reliable basis for stress field computation and interpretation in simulations employing machine-learning interatomic potentials.