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CATEGORIES:Machine learning in Physics\, Chemistry and Materi
als discussion group (MLDG)
SUMMARY:Representing many-body wave functions using Gaussi
an processes - Aldo Glielmo\, International School
for Advanced Studies (SISSA)
DTSTART;TZID=Europe/London:20200525T163000
DTEND;TZID=Europe/London:20200525T170000
UID:TALK142555AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/142555
DESCRIPTION:The dimension of the Fock space of N electrons gro
ws exponentially with N\, and developing compact r
epresentations that can capture the most important
correlations of many-body wave functions with pol
ynomial resources is hence a necessity. Traditiona
l representations (as for instance the Gutzwiller\
, the Jastrow\, and the EPS) directly reproduce a
specific set of low-order correlations that are de
emed important. Conversely\, parameterisations bas
ed on the use of neural networks (NN) architecture
s have no clear physical interpretation\, nonethel
ess they attracted a lot of attention for their fo
rmal systematic improvability.\n In my talk I wil
l present “Gaussian process states” (GPS)\, a nove
l framework for the construction of many-body stat
es based on Bayesian statistics and Gaussian proce
ss (GP) regression. Similarly to a NN representati
on\, GPS possesses the “universal approximator” pr
operty but\, differently from it\, can be interpre
ted in terms of physically meaningful correlations
. For instance\, under specific limits a GPS is ab
le to exactly reproduce Gutzwiller\, Jastrow and E
PS wave functions.\n I will introduce two numeric
al approaches to train a GPS: a “fragmentation” ap
proach\, and direct variational optimisation. Exte
nsive benchmarking on the Fermionic Hubbard model
in 1 and 2 spatial dimensions reveals the competit
iveness of the GPS framework\, which is found to a
chieve similar and often superior descriptions of
correlated quantum problems than existing state-of
-the-art approaches.
LOCATION:virtual ZOOM meeting ID: 263 591 6003\, https://zo
om.us/j/2635916003
CONTACT:Bingqing Cheng
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