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UID:news220@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20180716T175646
DTSTART;TZID=Europe/Zurich:20180504T110000
SUMMARY:Seminar in Numerical Analysis: Jan Hamaekers (Fraunhofer SCAI)
DESCRIPTION:In this talk\, we introduce a new scheme for the efficient nume
rical treatment of the electronic SchrÃ¶dinger equation for molecules. It
is based on the combination of a many-body expansion\, which corresponds t
o the so-called bond order dissection Anova approach\, with a hierarchy of
basis sets of increasing order. Here\, the energy is represented as a fin
ite sum of contributions associated to subsets of nuclei and basis sets in
a telescoping sum like fashion. Under the assumption of data locality of
the electronic density (nearsightedness of electronic matter)\, the terms
of this expansion decay rapidly and higher terms may be neglected. We furt
her extend the approach in a dimension-adaptive fashion to generate quasi-
optimal approximations\, i.e. a specific truncation of the hierarchical se
ries such that the total benefit is maximized for a fixed amount of costs.
This way\, we are able to achieve substantial speed up factors compared t
o conventional first principles methods depending on the molecular system
under consideration. In particular\, the method can deal efficiently with
molecular systems which include only a small active part that needs to be
described by accurate but expensive models. Finally\, we discuss to apply
such a multi-level many-body decomposition in the context of machine learn
ing for many-body systems.
X-ALT-DESC:In this talk\, we introduce a new scheme for the efficient numer
ical treatment of the electronic SchrÃ¶dinger equation for molecules. It i
s based on the combination of a many-body expansion\, which corresponds to
the so-called bond order dissection Anova approach\, with a hierarchy of
basis sets of increasing order. Here\, the energy is represented as a fini
te sum of contributions associated to subsets of nuclei and basis sets in
a telescoping sum like fashion. Under the assumption of data locality of t
he electronic density (nearsightedness of electronic matter)\, the terms o
f this expansion decay rapidly and higher terms may be neglected. We furth
er extend the approach in a dimension-adaptive fashion to generate quasi-o
ptimal approximations\, i.e. a specific truncation of the hierarchical ser
ies such that the total benefit is maximized for a fixed amount of costs.
This way\, we are able to achieve substantial speed up factors compared to
conventional first principles methods depending on the molecular system u
nder consideration. In particular\, the method can deal efficiently with m
olecular systems which include only a small active part that needs to be d
escribed by accurate but expensive models. Finally\, we discuss to apply s
uch a multi-level many-body decomposition in the context of machine learni
ng for many-body systems.
DTEND;TZID=Europe/Zurich:20180504T120000
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