This topic has been taken by Student 1 for 2017 Contribution
This page will provide information on how to model uncertainty using the MEAM parameter calibration (MPC) tool and Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS). On this page, the central finite difference approximation is used as an example to help users to understand how to model the uncertainty of the response of your system with respect to certain variables.
In this example, the "response" of our system will be the dislocation velocity determined from LAMMPS. Additionally, "variables" can be inputs that contribute to the response of your system. In this example, these variables will be will be the MEAM parameters that are used to input into LAMMPS.
The uncertainty of the response of your system can be approximated using a one-factor-at-atime perturbation methodology. This method uses the central difference approximation to estimate the sensitivity of your response with respect to input variables. This sensitivity can be expressed as:
where f() is the model function, Xi is the model input parameter, X0,i is the base value of a parameter, +/-i is the perturbation size around the base parameter, and DeltaXi is the difference between the perturbed input parameters. The perturbation size typically assumes a +/-1% perturbed factor. The uncertainty based on the sensitivity of an input can be determined from the following equation:
Calibrate your MEAM potential with respect to Density Functional Theory. This requires the use of elastic constants from experiments or literature to calibrate your material to DFT.