  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 we 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, GPYUMD, CALORINE, and PYNEP, which enable the integration of GPUMD
into Python workflows.
