# Berlin 2018 – wissenschaftliches Programm

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# MM: Fachverband Metall- und Materialphysik

## MM 52: Methods in Computational Materials Modelling (methodological aspects, numerics)

### MM 52.2: Vortrag

### Donnerstag, 15. März 2018, 10:30–10:45, TC 006

**A Preconditioning scheme for Minimum Energy Path finding methods.** — •Stela Makri^{1}, James Kermode^{1}, and Christoph Ortner^{2} — ^{1}Warwick Centre for Predictive Modelling, School of Engineering, University of Warwick, Coventry, UK — ^{2}Mathematics Institute, University of Warwick, Coventry, UK

In transition state theory, the study of thermally activated transitions between energy minima is achieved by finding transition paths connecting the minima. These paths provide information on the energy barrier and reaction rates of the system without going through long and expensive simulations. To find them, current techniques use steepest descent-like minimisation to relax a discretised initial guess. However, steepest descent typically gives slow convergence rates in the presence of ill-conditioned potentials. In this talk I will be discussing how to reduce the condition number of the potential of an arbitrary system and improve the convergence speed and robustness of transition path finding methods, using a preconditioning scheme.

Our key assumption is that the cost of constructing a preconditioner is much smaller than the cost of computing the potential; for density functional theory the cost of single point evaluations is much more expensive than the computation of a preconditioner and thus the proposed approach improves computing times significantly. We have developed a local preconditioning scheme, where the preconditioner acts as a coordinate transformation on the discrete images along the path and a global preconditioning scheme is currently in development, in which the entire path is preconditioned as one entity.