Artificial neural network potentials for mechanics and fracture dynamics of two-dimensional crystals ^**

Abstract

Understanding the mechanics and failure of materials at the nanoscale is critical for their engineering and applications. The accurate atomistic modeling of brittle failure with crack propagation in covalent crystals requires a quantum mechanics-based description of individual bond-breaking events. Artificial neural network potentials (NNPs) have emerged to overcome the traditional, physics-based modeling tradeoff between accuracy and accessible time and length scales. Previous studies have shown successful applications of NNPs for describing the structure and dynamics of molecular systems and amorphous or liquid phases of materials. However, their application to deformation and failure processes in materials is still uncommon. In this study, we discuss the apparent limitations of NNPs for the description of deformation and fracture under loadings and propose a way to generate and select training data for their employment in simulations of deformation and fracture simulations of crystals. We applied the proposed approach to 2D crystalline graphene, utilizing the density-functional tight-binding (DFTB) method for more efficient and extensive data generation in place of density functional theory (DFT). Then, we explored how the data selection affects the accuracy of the developed artificial NNPs. It revealed that NNP’s reliability should not only be measured based on the total energy and atomic force comparisons for reference structures but also utilize comparisons for physical properties, e.g., stress-strain curves and geometric deformation. In sharp contrast to popular reactive bond order potentials, our optimized NNP predicts straight crack propagation in graphene along both armchair and zigzag lattice directions, as well as higher fracture toughness of zigzag edge direction. Our study provides significant insight into crack propagation mechanisms on atomic scales and highlights strategies for NNP developments of broader materials.

Active learning of neural network potentials for rare events

“…These observations are consistent with a previous study on graphene fracture. 44 The trained model from the equilibrium states could not describe the graphene's fracture. Also, the data obtained from a single fracture simulation is insufficient to train the NNP to accurately describe the properties of graphene fracture, e.g.…”

“…We performed the SMD simulation with trained NNPs under the same conditions, using a previously developed interface between PyTorch and LAMMPS. 44…”

“…The basic training conditions are the same as in the previous study. 44 We trained parameters with 300 epochs and took the best parameters for the MSE of energy with the validation set during the epochs. We did not prepare a test set during the active learning iterations.…”

“…A previous study applied a similar approach to graphene fracture to address the data imbalance problem. 44…”