Uncertainty quantification for classical effective potentials: an extension to potfit

Abstract

Effective potentials are an essential ingredient of classical molecular dynamics (MD) simulations. Little is understood of the consequences of representing the complex energy landscape of an atomic configuration by an effective potential or force field containing considerably fewer parameters. The probabilistic potential ensemble method has been implemented in the potfit force matching code. This introduces uncertainty quantification into the interatomic potential generation process. Uncertainties in the effective potential are propagated through MD to obtain uncertainties in quantities of interest, which are a measure of the confidence in the model predictions.We demonstrate the technique using three potentials for nickel: two simple pair potentials, Lennard-Jones and Morse, and a local density dependent embedded atom method (EAM) potential. A potential ensemble fit to density functional theory (DFT) reference data is constructed for each potential to calculate the uncertainties in lattice constants, elastic constants and thermal expansion. We quantitatively illustrate the cases of poor model selection and fit, highlighted by the uncertainties in the quantities calculated. This shows that our method can capture the effects of the error incurred in quantities of interest resulting from the potential generation process without resorting to comparison with experiment or DFT, which is an essential part to assess the predictive power of MD simulations.

Managing uncertainty in data-derived densities to accelerate density functional theory

“…Evaluating an error or measure of confidence in a data-driven prediction like n(x) is a well studied problem [15,16]. Applications of uncertainty quantification have recently begun appearing in materials science, with some even in DFT, such as the linear model exchange correlation functional of Aldegunde et al [17][18][19][20][21]. In this work, we show that useful applications of a predictive uncertainty in n(x) can be realised for just one of many possible approaches.…”

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

“…Furthermore, quantification of uncertainty due to the potential fitting reference set [57] was augmented by propagation of parametric uncertainties to MD outputs [58]. Recent efforts have focused on fitting interatomic potentials to data and subsequently quantifying the uncertainty [59]. These efforts contributed to the uncertainty quantification and potential development by providing an open source implementation of the framework proposed by Frederiksen et al [54].…”

“…A good measure of the confidence in the model predictions consists of evaluating the uncertainty in the effective potential. Longbottom, et al, have demonstrated this technique using three potentials for nickel: two simple pair potentials, Lennard-Jones and Morse, and a local density dependent embedded atom method potential [59]. They were successful in developing a potential ensemble fit to DFT calibration data to calculate the uncertainties in lattice constants, elastic constants and thermal expansion of nickel.…”

A stochastic framework for atomistic fracture

“…A typical empirical potential has between 2 and 11 parameters (rising to > 1000 for modern machine-learning potentials), and the highly nonlinear nature of the overall model necessitates quantifying the uncertainty in their choice and how this propagates to the quantities of interest. In the literature, this is usually done by employing a Bayesian framework, in which one assumes some prior probability distributions for the parameters, which are subsequently updated using available datasets originating from experiments or higher-level theories [10,21,33]. However, two main issues can potentially arise with this approach.…”

“…However, two main issues can potentially arise with this approach. Firstly, the prior distribution of each parameter is typically taken to be a Gaussian (e.g., in [10,21,33]), due to the seemingly reasonable assumption that errors in the reference dataset are independent. This may not necessarily hold true, depending on the physical constraints present in the model, such as, for example, the fact that some parameters have positive values.…”