3 research outputs found
Development of an exchange–correlation functional with uncertainty quantification capabilities for density functional theory
This paper presents the development of a new exchange–correlation functional from the point of view of machine learning. Using atomization energies of solids and small molecules, we train a linear model for the exchange enhancement factor using a Bayesian approach which allows for the quantification of uncertainties in the predictions. A relevance vector machine is used to automatically select the most relevant terms of the model. We then test this model on atomization energies and also on bulk properties. The average model provides a mean absolute error of only 0.116 eV for the test points of the G2/97 set but a larger 0.314 eV for the test solids. In terms of bulk properties, the prediction for transition metals and monovalent semiconductors has a very low test error. However, as expected, predictions for types of materials not represented in the training set such as ionic solids show much larger errors
Uncertainty quantification for classical effective potentials: an extension to potfit
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.Comment: 10 pages, 3 figure