Hierarchical Bridging Between Ab Initio and Atomistic Level Computations: Sensitivity and Uncertainty Analysis for the Modified Embedded-Atom Method (MEAM) Potential (Part B)

Hughes, Justin M.; Horstemeyer, M.F.; Cariño, Ricolindo L.; Sukhija, Nitin; Lawrimore, William B.; Kim, Seong‐Gon; Baskes, M. I.

doi:10.1007/s11837-014-1205-7

Cited by 14 publications

(7 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this work, we could construct a transferable potential of aluminum partly because it has a basic reference database with small uncertainties. Among the basic reference database, the uncertainty of single vacancy formation energy is the largest, which can be as large as 10.96% [26]. Thus, it is necessary to discuss the sensitivity of the extrapolated qualities of constructed potentials to the uncertainties of single vacancy formation energy.…”

Section: Sensitivity Of Extrapolated Results Of Potentials To the Ref...mentioning

confidence: 99%

“…Obviously, sensitivities of extrapolated results to uncertainties of the SRD are main obstacles to obtain a transferable potential. Recently, studies [26,27] on the sensitivities of the modified EAM potential of aluminum to the input uncertainties show that all modified EAM parameters interdependently influence the model outputs to varying degrees. That is to say, extrapolated results are insensitive to some FPs which may be not necessary for the potential.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A new embedded-atom method approach based on thepth moment approximation

Wang¹,

Zhu²,

Xiao

et al. 2016

J. Phys.: Condens. Matter

View full text Add to dashboard Cite

Large scale atomistic simulations with suitable interatomic potentials are widely employed by scientists or engineers of different areas. The quick generation of high-quality interatomic potentials is urgently needed. This largely relies on the developments of potential construction methods and algorithms in this area. Quantities of interatomic potential models have been proposed and parameterized with various methods, such as the analytic method, the force-matching approach and multi-object optimization method, in order to make the potentials more transferable. Without apparently lowering the precision for describing the target system, potentials of fewer fitting parameters (FPs) are somewhat more physically reasonable. Thus, studying methods to reduce the FP number is helpful in understanding the underlying physics of simulated systems and improving the precision of potential models. In this work, we propose an embedded-atom method (EAM) potential model consisting of a new manybody term based on the pth moment approximation to the tight binding theory and the general transformation invariance of EAM potentials, and an energy modification term represented by pairwise interactions. The pairwise interactions are evaluated by an analytic-numerical scheme without the need to know their functional forms a priori. By constructing three potentials of aluminum and comparing them with a commonly used EAM potential model, several wonderful results are obtained. First, without losing the precision of potentials, our potential of aluminum has fewer potential parameters and a smaller cutoff distance when compared with some constantly-used potentials of aluminum. This is because several physical quantities, usually serving as target quantities to match in other potentials, seem to be uniquely dependent on quantities contained in our basic reference database within the new potential model. Second, a key empirical parameter in the embedding term of the commonly used EAM model is found to be related to the effective order of moments of local density of states. This may provide a way to improve the precision of EAM potentials further through more precise approximations to tight binding theory. In addition, some critical details about construction procedures are discussed.

show abstract

Section: Sensitivity Of Extrapolated Results Of Potentials To the Ref...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A new embedded-atom method approach based on thepth moment approximation

Wang¹,

Zhu²,

Xiao

et al. 2016

J. Phys.: Condens. Matter

View full text Add to dashboard Cite

show abstract

“…Given the parametric uncertainties, they can then be propagated to other quantities of interest, for example as in Ref. 14. This entire process is illustrated in Fig.…”

Section: Introductionmentioning

confidence: 99%

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

Kurniawan,

Petrie,

Williams

et al. 2021

Preprint

View full text Add to dashboard Cite

In this paper, we consider the problem of quantifying parametric uncertainty in classical empirical interatomic potentials (IPs) using both Bayesian (MCMC) and Frequentist (profile likelihood) methods. We interface these tools with the Open Knowledgebase of Interatomic Models (OpenKIM) and study three models based on the Lennard-Jones, Morse, and Stillinger-Weber potentials. We confirm that IPs are typically sloppy, i.e., insensitive to coordinated changes in some parameter combinations. Because the inverse problem in such models is ill-conditioned, parameters are unidentifiable which present challenges for traditional statistical methods as we demonstrate and interpret within both Bayesian and Frequentist frameworks. We use information geometry to illuminate the underlying cause of this phenomenon and show that IPs have global properties similar to those of sloppy models from fields such as systems biology, power systems, and critical phenomena. IPs correspond to bounded manifolds with a hierarchy of widths, leading to low effective dimensionality in the model. We show how information geometry can motivate new, natural parameterizations that improve the stability and interpretation of UQ analysis and further suggest simplified, less-sloppy models.

show abstract

“…Previous 0 K sensitivity analyses have been performed using MEAM potentials (20)(21)(22). In addition, there have also been attempts to quantify MEAM uncertainty using confidence intervals around specific values to obtain an uncertainty interval for various ground state properties (23,24). To our knowledge, this is the first sensitivity analysis for elemental thermal properties and alloys, for which a new method of analyzing the effects that parameters have on the alloy properties has been developed.…”

Section: Introductionmentioning

confidence: 99%

Understanding the uncertainty of interatomic potentials’ parameters and formalism

Moore

Deo

Baskes

et al. 2017

Computational Materials Science

View full text Add to dashboard Cite

A sensitivity analysis of the modified embedded atom method (MEAM) potential for bodycentered-cubic uranium and zirconium was performed in order to examine and understand the uncertainty in the parameters and formalism of the interatomic potential. The sensitivity analysis was conducted using one-at-a-time (OAT) sampling of the parameters and how they affected the ground state, thermal, and alloy structural and thermodynamic properties. The performed analysis was able to uncover the properties that can be easily varied or adjusted like the lattice constant, and the properties that had little variance like the heat capacity. The observed analysis on the ground state properties was found to correspond well with previously published results, after which the thermal and alloy properties were examined. A new method of categorizing changes in the alloy properties was developed that allows for the discrimination of bonding behaviors, determining if the strength of the bonding between atoms changed or if the manner in which they were bonded together changed.

show abstract

Hierarchical Bridging Between Ab Initio and Atomistic Level Computations: Sensitivity and Uncertainty Analysis for the Modified Embedded-Atom Method (MEAM) Potential (Part B)

Cited by 14 publications

References 6 publications

A new embedded-atom method approach based on thepth moment approximation

A new embedded-atom method approach based on thepth moment approximation

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

Understanding the uncertainty of interatomic potentials’ parameters and formalism

Contact Info

Product

Resources

About