Dear all,

We are inviting applicants for the following open position (see below).

With my best regards, Ivan Kondov

PhD Position (3 years 75% salary level E13)

Uncertainty quantification in multiscale materials modelling

Courses: mathematics, physics, computational science, materials science

Topic description

Uncertainty quantification has been adopted for single-scale methods such as density functional theory (DFT), force field methods and coarse-grained modeling. These methods, although widely applied, are still no black-box methods. Their successful application still requires a very good knowledge of their strengths and shortcomings. Moreover, combining these methods raises the question about propagation of uncertainty across the time and length scales.

Application 1 (in project P1 "Friction at solid--liquid interfaces") Quantities obtained from molecular dynamics (MD) simulations fluctuate naturally because of thermal effects. A key aspect of our continuum-coupling scheme will therefore be to disentangle thermal fluctuations from uncertainties. Methods for local and global sensitivity analysis have to be developed to determine and discriminate the errors caused by the MD simulations. This requires the development of a machine learning (ML) regression scheme that predicts amplitudes of thermal fluctuations, e.g. of the stress tensor, in addition to mean values as well as their respective uncertainties for active learning scenarios. With these amplitudes, the continuum solver will be extended to incorporate these fluctuations. This requires a reformulation of the height-averaged continuum equation, starting from fluctuating hydrodynamics. A key challenge here will be the analytical computation of statistical fluctuations of the averaged field that needs to fulfil some form of fluctuation-dissipation theorem.

Application 2 (in project P3 "Single-site catalysis in porous materials") Reaction and diffusion rates, computed by either DFT or machine learning force fields (MLFF), contain uncertainties of various kinds that are propagated through the kinetic Monte Carlo (KMC) simulation. Especially when two or more KMC rates are produced using a common method and input data that may result in error cancellation or accumulation. The effects of such correlated uncertainties will be investigated using global sensitivity analysis. This will make possible to identify the critical uncertainties in the most influential rates determining the kinetic pathway. We will analyze the uncertainties affecting the predicted effect of confinement, as well as uncertainties arising from the DFT calculations.

Requirements

Knowledge or experience in at least one of these methodological fields will be an advantage for the candidate: mathematical modelling, machine learning / statistical modeling, and uncertainty quantification.

Partners

This thesis will be carried out in the framework of the interdisciplinary Research Training Group 2450 "Tailored Scale-Bridging Approaches to Computational Nanoscience" in close collaboration with partner PhD students within the training group.

Contact

Dr. Ivan Kondov Steinbuch Centre for Computing Karlsruhe Institute of Technology ivan.kondov@kit.edu