Hybrid machine-learning-assisted quantification of the compound internal and external uncertainties of graphene: towards inclusive analysis and design

Abstract

Molecular dynamics (MD) simulations have emerged to be a vital tool for the analysis of nanoscale materials like graphene. However, the reliability of the results derived from MD simulations depends on the adopted inter-atomic potential (IP), which is mathematically fitted to the data obtained from first principles approaches or experiments. There exists a significant scope of uncertainty associated with the IP parameters. Such internal uncertainties, together with the effect of stochastic external parameters like temperature and strain rate can trigger an augmented random deviation in the output mechanical responses. With the aim of developing an inclusive analysis and design paradigm, we have systematically quantified the effect of the uncertainties associated with the internal parameters (Tersoff IP parameters) and external parameters (temperature and strain rate) individually, and their compound effect on the mechanical properties of graphene. In establishing the complete probabilistic descriptions of the response quantities corresponding to different levels of source uncertainties, we show that a coupled machine learning-based Monte Carlo simulation approach could lead to significant computational efficiency without compromising the accuracy of the results. The study reveals that, in general, the internal parameters are more sensitive than the external parameters. Among the inter-atomic parameters, λ₁ and λ₂ are found to be the most sensitive, while the temperature is found to be more sensitive than the strain rate among the external parameters. The cohesive energy is noted to be dependent only on the inter-atomic potential parameters, while the fracture strength depends on both the internal and external input parameters. The numerically quantifiable outcomes of this study will improve and bring new perspectives in the inclusive analysis and design of various graphene-based devices and systems, including the effect of inherent uncertainties and their relative sensitivity.