Predicting nanoscale stress-strain curves: A Gaussian processes within a Bayesian framework

This study introduces an innovative method for probabilistically predicting the stress–strain curves of nanoscale materials, with a specific focus on material volume. To achieve this, molecular dynamics (MD) simulations were meticulously conducted across various material sizes to gather stress–strain data. Subsequently, a sophisticated approach was employed, integrating a Gaussian process (GP) within a Bayesian framework to comprehensively model the stress–strain behavior and forecast the complete stress–strain profiles for materials of different sizes. What sets this probabilistic machine learning algorithm apart is its capacity to not only offer precise predictions of material behavior but also to provide a detailed assessment of uncertainty. This feature ensures its effectiveness in generating accurate forecasts of stress–strain characteristics, surpassing the conventional limitations posed by material volume encountered in MD simulations. In doing so, it addresses the crucial challenge of size restrictions inherent to atomistic simulations. To rigorously validate the capabilities of this methodology, we conducted extensive testing using pure copper as our experimental material, benefitting from its comprehensive repository of stress–strain data. It is important to note that this methodology is not restricted to any specific material; instead, it serves as a robust and versatile tool for probabilistically predicting the mechanical properties of nanoscale materials. Consequently, this approach holds immense potential for diverse applications within the field of materials science and engineering, offering researchers an invaluable means to gain insights into the behavior of materials at the nanoscale.