Application and acceleration of machine learning potential construction using farthest point sampling: A case study of carbon nanotubes

In molecular dynamics simulations, potential functions are mathematical expressions that describe the interactions between particles in materials. As an emerging material, carbon nanotubes (CNTs) are widely applied in fields such as biosensing, electronic devices, composite materials, and more. An accurate carbon potential function is a critical prerequisite for obtaining the structural properties of carbon nanomaterials. Recently, molecular dynamics simulations of carbon based on machine learning potentials (MLPs) have been proven to be highly effective, owing to the rapid development of computational materials science and machine learning (ML). However, the existing machine learning model training data for CNTs fails to cover all possible configurations (such as different chiralities, diameters, and defects), and is not entirely satisfactory in simulating the performance of CNTs. In this work, based on deep neural network methods, we utilized principal component analysis and farthest point sampling to thoroughly explore the phase space of various types of carbon nanotubes, developing an accurate deep potential (DP) model for carbon nanotubes. To ensure the accuracy of the interatomic potentials of carbon nanotubes, we cleverly constructed the most precise and comprehensive initial dataset of carbon nanotubes through data augmentation techniques. This dataset includes 504 structural configurations, covering various types such as perturbations, double-walled, multi-walled, and point defects. The new dataset was constructed by combining active learning with farthest point sampling methods. We selected 15 representative structures to explore specific regions of the potential energy surface (PES), sampling 900,000 structures, which were screened and then added to the dataset. The carbon nanotube potential function successfully reproduces the physical and thermodynamic properties of carbon nanotubes near a temperature of 0–1000 K with precision close to that of DFT calculations. Additionally, this potential function exhibits superior generalization capabilities. This work establishes a high-precision, low-cost machine learning interatomic potential for carbon nanotubes, opening up new possibilities for the exploration and understanding of carbon-based nanomaterials.