Spectral decomposition of thermal conductivity: Comparing velocity decomposition methods in homogeneous molecular dynamics simulations

The design of applications, especially those based on heterogeneous integration, must rely on detailed knowledge of material properties, such as thermal conductivity (TC). To this end, multiple methods have been developed to study TC as a function of vibrational frequency. Here, we compare three spectral TC methods based on velocity decomposition in homogenous molecular dynamics simulations: Green-Kubo modal analysis (GKMA), the spectral heat current (SHC) method, and a method we propose called homogeneous nonequilibrium modal analysis (HNEMA). First, we derive a convenient per-atom virial expression for systems described by general many-body potentials, enabling compact representations of the heat current, each velocity decomposition method, and other related quantities. Next, we evaluate each method by calculating the spectral TC for carbon nanotubes, graphene, and silicon. We show that each method qualitatively agrees except at optical phonon frequencies, where a combination of mismatched eigenvectors and a large density of states produces artificial TC peaks for modal analysis (MA) methods. Our calculations also show that the HNEMA and SHC methods converge much faster than the GKMA method, with the SHC method being the most computationally efficient. Finally, we demonstrate that our MA implementation in the Graphics Processing Units Molecular Dynamics code on a single graphics processing unit is over 1000 times faster than the existing implementation in the Large-scale Atomic/Molecular Massively Parallel Simulator code on one central processing unit

GPUMD: A package for constructing accurate machine-learned potentials and performing highly efficient atomistic simulations

We present our latest advancements of machine-learned potentials (MLPs) based on the neuroevolution potential (NEP) framework introduced in Fan et al. [Phys. Rev. B 104, 104309 (2021)] and their implementation in the open-source package gpumd. We increase the accuracy of NEP models both by improving the radial functions in the atomic-environment descriptor using a linear combination of Chebyshev basis functions and by extending the angular descriptor with some four-body and five-body contributions as in the atomic cluster expansion approach. We also detail our efficient implementation of the NEP approach in graphics processing units as well as our workflow for the construction of NEP models and demonstrate their application in large-scale atomistic simulations. By comparing to state-of-the-art MLPs, we show that the NEP approach not only achieves above-average accuracy but also is far more computationally efficient. These results demonstrate that the gpumd package is a promising tool for solving challenging problems requiring highly accurate, large-scale atomistic simulations. To enable the construction of MLPs using a minimal training set, we propose an active-learning scheme based on the latent space of a pre-trained NEP model. Finally, we introduce three separate Python packages, viz., gpyumd, calorine, and pynep, that enable the integration of gpumd into Python workflows