Berlin 2018 – wissenschaftliches Programm

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MM: Fachverband Metall- und Materialphysik

MM 57: Methods in Computational Materials Modelling (methodological aspects, numerics)

MM 57.4: Vortrag

Donnerstag, 15. März 2018, 12:30–12:45, TC 006

A Compressed Sensing Approach to Kohn-Sham Density Functional Theory — •Ingo Roth¹, Adrian Steffens^1,2, Christian Krumnow¹, Luca Ghiringhelli², Matthias Scheffler², and Jens Eisert¹ — ¹Dahlem Center for Complex Quantum Systems, FU Berlin, Germany — ²Fritz-Haber-Institut der Max-Planck-Gesellschaft, Berlin, Germany

In density-functional theory calculations, the choice of basis sets plays a crucial role, determining the accuracy and computational cost of the simulation. The use of standardized basis sets and schemes which exploit the locality of the problem explicitly by assuming the Fock matrix to be banded often restrict the allowed states too much. Moreover, choosing an optimal basis set is a nontrivial task for many systems of interest, and large basis sets to compensate for this do not only increase computational time, but may also lead to numerical instability. In a more flexible approach, we propose a scheme that employs central notions of compressed sensing, a signal processing paradigm that has revolutionized the recovery of signals by efficiently identifying their underlying sparsity patterns, which makes it possible to massively undersample, yet fully recover a signal. In this spirit, we have developed an algorithm based on multi-task regularized Stiefel-manifold optimization that enforces sparsity basis function coefficients, thus identifying those basis functions that carry the most relevant information of the system.