Uncertainty quantification in non-equilibrium molecular dynamics simulations of thermal transport

Abstract

Bulk thermal conductivity estimates based on predictions from non-equilibrium molecular dynamics (NEMD) using the so-called direct method are known to be severely underpredicted since finite simulation length-scales are unable to mimic bulk transport. Moreover, subjecting the system to a temperature gradient by means of thermostatting tends to impact phonon transport adversely. Additionally, NEMD predictions are tightly coupled with the choice of the inter-atomic potential and the underlying values associated with its parameters. In the case of silicon (Si), nominal estimates of the Stillinger-Weber (SW) potential parameters are largely based on a constrained regression approach aimed at agreement with experimental data while ensuring structural stability. However, this approach has its shortcomings and it may not be ideal to use the same set of parameters to study a wide variety of Si-based systems subjected to different thermodynamic conditions. In this study, NEMD simulations are performed on a Si bar to investigate the impact of bar-length, and the applied thermal gradient on the discrepancy between predictions and the available measurement for bulk thermal conductivity at 300 K by constructing statistical response surfaces at different temperatures. The approach helps quantify the discrepancy, observed to be largely dependent on the system-size, with minimal computational effort. A computationally efficient approach based on derivative-based sensitivity measures to construct a reduced-order polynomial chaos surrogate for NEMD predictions is also presented. The surrogate is used to arXiv:1805.00118v2 [physics.comp-ph]

Uncertainty quantification for classical effective potentials: an extension to potfit

“…There has also been work toward the quantification of uncertainty due to the potential fitting reference set [4], as well as a proposed framework to efficiently propagate parameter uncertainties to molecular dynamics (MD) outputs [5]. More specifically, quantification of parameter uncertainty for single potentials has been undertaken in a handful of cases [6][7][8][9]. We add to the growing body of uncertainty quantification (UQ) work in potential development and application by providing an open source implementation of the framework in [1] for use in future potential development projects.…”

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

“…These potentials are categorized as cluster potentials. Given a system with N atoms, the total potential energy, (18) where φ n denotes the n-body potential function and r i is the position of atom i.…”

“…In materials science, Markov Chain Monte Carlo (MCMC) sampling of the Bayesian posterior is the most common approach. 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 .…”

Uncertainty Quantification in Atomistic Modeling of Metals and Its Effect on Mesoscale and Continuum Modeling: A Review

“…The quantification of parametric uncertainty for single potentials has been undertaken in several cases [52,53] while Bayesian frameworks have also been proposed for a variety of interatomic models and force fields [54,55,56]. Furthermore, quantification of uncertainty due to the potential fitting reference set [57] was augmented by propagation of parametric uncertainties to MD outputs [58].…”

“…The approach consists of properly randomizing a reduced-order basis, obtained by the method of snapshots in the configuration space. A multi-step strategy to identify the hyperparameters in the stochastic reduced-order basis was further introduced, enabling the robust, simultaneous treatment of parametric uncertainties on a set of potentials [62] Furthermore, uncertainty quantification in non-equilibrium phenomena, such as thermal transport, was studied to estimate bulk thermal conductivity via non-equilibrium molecular dynamics (NEMD) [52].…”