Quantifying Parameter Sensitivity and Uncertainty for Interatomic Potential Design: Application to Saturated Hydrocarbons

Abstract

The research objective herein is to understand the relationships between the interatomic potential parameters and properties used in the training and validation of potentials, specifically using a recently developed modified embedded-atom method (MEAM) potential for saturated hydrocarbons (C–H system). This potential was parameterized to a training set that included bond distances, bond angles, and atomization energies at 0 K of a series of alkane structures from methane to n-octane. In this work, the parameters of the MEAM potential were explored through a fractional factorial design and a Latin hypercube design to better understand how individual MEAM parameters affected several properties of molecules (energy, bond distances, bond angles, and dihedral angles) and also to quantify the relationship/correlation between various molecules in terms of these properties. The generalized methodology presented shows quantitative approaches that can be used in selecting the appropriate parameters for the interatomic potential, selecting the bounds for these parameters (for constrained optimization), selecting the responses for the training set, selecting the weights for various responses in the objective function, and setting up the single/multi-objective optimization process itself. The significance of the approach applied in this study is not only the application to the C–H system but that the broader framework can also be easily applied to any number of systems to understand the significance of parameters, their relationships to properties, and the subsequent steps for designing interatomic potentials under uncertainty.

Interatomic Potential for Hydrocarbons on the Basis of the Modified Embedded-Atom Method with Bond Order (MEAM-BO)

“…The overall parametrization procedure and the associated parameters to be determined are listed in Table 7. A set of parameters at each step is chosen through a sensitivity analysis similar to the work of Tschopp et al 41 All procedures described herein were carried out using Matlab, and its built-in function fminsearch was used for the downhill simplex method used.…”

Bayesian, frequentist, and information geometric approaches to parametric uncertainty quantification of classical empirical interatomic potentials

“…Being a Bayesian method, this requires a prior distribution, and several prior distributions have been used, including uniform [15][16][17][18][19][20][21] , normal 22 , Jeffreys prior 23 , and maximum entropy 24 . Other approaches to UQ include: F -statistics estimations 25 , ANOVA-based methods 26 , and multi-objective optimization 27 . Other fields have used the profile likelihood method [28][29][30] , which to the best of our knowledge has not yet been applied to IPs.…”

Quantifying uncertainty in the process-structure relationship for Al–Cu solidification

“…The major sources of uncertainty in molecular dynamics are inaccurate interatomic potentials and the bias introduced in simulated small sizes and short time scales. UQ methods such as polynomial chaos expansion [11,12], statistical regression [13], Bayesian calibration [14][15][16][17][18], interval bound analysis [19,20], and local SA and perturbation [21,22] have been applied to quantify simulation errors. The uncertainty in kinetic Monte Carlo simulation is mainly due to event independence assumption, incomplete knowledge of event catalog, and imprecise kinetic rates.…”