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CATEGORIES:Lectures, Symposia, Etc.
DESCRIPTION:Translation and Rotation Equivariant Normalizing Flow (TRENF) f
or OptimalCosmological Analysis\n\nOur universe is homogeneous and isotropi
c\, and its perturbations are translation and rotation equivariant. We deve
lop a generative Normalizing Flow(NF) architecture which explicitly incorpo
rates these symmetries\, defining the data likelihood via a sequence of Fou
rier space based convolutions and non linear transforms\, evaluating their
Jacobian at each layer. This allows to train the NF by maximizing the data
likelihood p(x|y) as a function of the labels y\, such as cosmological para
meters. In contrast to other generative models the NF approach has no loss
of information since it preserves the full dimensionality of the data\, and
gives direct access to the data likelihoodp(x|y). We apply this to outputs
of cosmological N-body simulations and show that the summary statistics of
the generated samples agree well with the simulations. We show that the re
verse mapping is visually indistinguishable from a Gaussian white noise: wh
en this is perfectly achieved the resulting p(x|y) likelihood analysis beco
mes optimal. On simple Gaussian examples we show that this approach maximiz
es the information in the data and saturates the Fisher information content
in the labels y. On N-body simulation outputs we show that this leads to s
ignificant improvements in constraining power over the standard summary sta
tistics such as the power spectrum. Finally\, we develop a generalization o
f this NF that can handle effects that break the symmetry of the data\, suc
h as the survey mask.
DTEND:20210917T170000Z
DTSTAMP:20220525T064738Z
DTSTART:20210917T160000Z
LOCATION:
SEQUENCE:0
SUMMARY: Astro Lunch: Biwei Dai
UID:tag:localist.com\,2008:EventInstance_37811874198690
URL:https://calendar.pitt.edu/event/astro_lunch_adam_broussard_rutgers
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