Toward nano-scale data-driven constitutive rules by combination of molecular dynamics and generalized additive models

Abstract

The advanced statistical learning method is rarely used in the field of nano-scaled models created using molecular dynamics simulations. This study will outline how to take benefits from the data collected from molecular dynamics simulation and create a surrogate model by relatively reputed but novel to nanoscale models by using a generalized additive model. Using amorphous metallic glass Cu_64 Zr_36 as a base material, a constitutive rule for a particular cooling rate, strain rate, and the sample size is found out. We also extracted sectional information from the given nanoscale model. We used it to form constitutive rules for several sections out of the nanoscale model that was evaluated while strain-induced uniaxial loading being applied to the complete model. This showed how various parameters affect the stress experienced by individual sections within the model itself. The database was compiled based on these relationships, and this spearheads the data-driven statistical learning approach to create the best possible Generalized Additive Model. Randomized 70 % of the database is used for training, and the remaining randomized 30% dataset validates the best possible GAM. We also see through plots and error estimation as to how close our surrogate model becomes. We have used a relatively new smooth layered 3D plot for bivariate models to see which covariates give better representation and less residual error by visualization, which is again a novel attempt towards nano-scaled molecular dynamics simulation-generated data. Results suggest that thin plate regression spline-based GAM can be used to make a good prediction model from data generated through molecular dynamics simulation for constitutive rules. However, better datasets can give an even closer prediction, which could be seen in lack of straight-line towards the beginning of QQ plot owed to lack of valuable data at that region. Similarly, better empirical relationships could increase the accuracy of the information index, which is used as one of the covariates. Other parameters like cooling rate, sample size, and so on that affect the constitutive rules can be included in creating GAM, which will be evaluated in future studies. The role of shear band in affecting the confinement model that later makes the basis for information index is also open for later findings.