We develop a neuroevolution-potential (NEP) framework for generating neural network-based machine-learning potentials. They are trained using an evolutionary strategy for performing large-scale molecular dynamics (MD) simulations. A descriptor of the atomic environment is constructed based on Chebyshev and Legendre polynomials. The method is implemented in graphic processing units within the open-source gpumd package, which can attain a computational speed over ${10}^7$ atom-step per second using one Nvidia Tesla V100. Furthermore, per-atom heat current is available in NEP, which paves the way for efficient and accurate MD simulations of heat transport in materials with strong phonon anharmonicity or spatial disorder, which usually cannot be accurately treated either with traditional empirical potentials or with perturbative methods.

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.

We derive expressions of interatomic force and heat current for many-body potentials such as the Tersoff, the Brenner, and the Stillinger-Weber potential used extensively in molecular dynamics simulations of covalently bonded materials. Although these potentials have a many-body nature, a pairwise force expression that follows Newton's third law can be found without referring to any partition of the potential. Based on this force formula, a stress applicable for periodic systems can be unambiguously defined. The force formula can then be used to derive the heat current formulas using a natural potential partitioning. Our heat current formulation is found to be equivalent to most of the seemingly different heat current formulas used in the literature, but to deviate from the stress-based formula derived from two-body potential. We validate our formulation numerically on various systems described by the Tersoff potential, namely three-dimensional silicon and diamond, two-dimensional graphene, and quasi-one-dimensional carbon nanotube. The effects of cell size and production time used in the simulation are examined.

The standard equilibrium Green–Kubo and nonequilibrium molecular dynamics (MD) methods for computing thermal transport coefficients in solids typically require relatively long simulation times and large system sizes. To this end, we revisit here the homogeneous nonequilibrium MD method by Evans [ Phys. Lett. A 91, 457 (1982)] and generalize it to many-body potentials that are required for more realistic materials modeling. We also propose a method for obtaining spectral conductivity and phonon mean-free path from the simulation data. This spectral decomposition method does not require lattice dynamics calculations and can find important applications in spatially complex structures. We benchmark the method by calculating thermal conductivities of three-dimensional silicon, two-dimensional graphene, and a quasi-one-dimensional carbon nanotube and show that the method is about one to two orders of magnitude more efficient than the Green–Kubo method. We apply the spectral decomposition method to examine the long-standing dispute over thermal conductivity convergence vs divergence in carbon nanotubes.

Machine-learned potentials (MLPs) have exhibited remarkable accuracy, yet the lack of general-purpose MLPs for a broad spectrum of elements and their alloys limits their applicability. Here, we present a promising approach for constructing a unified general-purpose MLP for numerous elements, demonstrated through a model (UNEP-v1) for 16 elemental metals and their alloys. To achieve a complete representation of the chemical space, we show, via principal component analysis and diverse test datasets, that employing one-component and two-component systems suffices. Our unified UNEP-v1 model exhibits superior performance across various physical properties compared to a widely used embedded-atom method potential, while maintaining remarkable efficiency. We demonstrate our approach’s effectiveness through reproducing experimentally observed chemical order and stable phases, and large-scale simulations of plasticity and primary radiation damage in MoTaVW alloys.