Uncertainty quantification in diffusion

kinisi is an open-source package focussed on accurately quantifying the uncertainty in atomic and molecular displacements, and using this to more completely understanding diffusion in materials.

Bootstrapping

kinisi uses a custom bootstrapping method to evaluate distribution of the mean-squared displacement at a particular timestep length. This resampling is performed until the distribution is found to be normal, or a user-controlled threshold is reached.

Diffusion estimation

A diffusion distribution is evaluated using a generalised least squares approach to modelling the Einstein relation to the data. This uses a covariance matrix defined based on the bootstrapped uncertainties for each MSD. This approach allows an estimate of the true displacement to be found from an infinitely long simulation. Note, this methodology is unpublished and results from it should be considered with great caution.

Uncertainty propagation

The uravu.relationship.Relationship class is leveraged to propagate the uncertainty in the diffusion coefficient using Bayesian inference, allowing the determination of the uncertainty in the activation energy from either an Arrhenius or a super-Arrhenius relationship. Finally, it is possible to use uravu to perform Bayesian model selection between the different temperature dependent relationships.

Brief tutorials showing how kinisi may be used in the study of an VASP Xdatcar file can be found in the tutorials.

Contributors

Andrew R. McCluskey | Benjamin J. Morgan

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