Redshift surveys in a nutshell
Learning summary statistics with ML
Carolina Cuesta-Lazaro
19th January 2022 - Waterloo Astronomy Seminar
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Collaborators: Cheng-Zong Ruan, Yosuke Kobayashi, Alexander Eggemeier, Pauline Zarrouk, Sownak Bose, Takahiro Nishimichi, Baojiu Li, Carlton Baugh
The golden days of Cosmology:
A five parameter Universe
Initial Conditions
Dynamics
Dark energy
Dark matter
Ordinary matter
Amplitude initial density field
Scale dependence
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Linear
Credit: NASA / WMAP SCIENCE TEAM
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GALAXY CLUSTERING
GRAVITATIONAL WAVES
GRAVITATIONAL LENSING
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Early Universe
~linear
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Gravity
Late Universe
Non-linear
Credit: S. Codis+16
Non-linearity = PT predictions inaccurate
Credit: S. Codis+16
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Early Universe
~linear
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Gravity
Late Universe
Non-linear
Credit: S. Codis+16
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Non-Guassianity
Second moment not optimal
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Machine Learning as a solution to
- Non-linearities Produce accurate predictions based on N-body simulations
- Non-Gaussianity Extract cosmological information at the field level
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Space-time
geometetry
Energy content
Adding new degrees of freedom
- To the energy content (dynamic) DARK ENERGY
- To the way space-time geometry reacts to the energy content MODIFIED GRAVITY (FIFTH FORCES)
?
Fifth forces modify structure growth
GROWTH
- GRAVITY
- FIFTH FORCE
+ EXPANSION
Credit: Cartoon depicting Willem de Sitter as Lambda from Algemeen Handelsblad (1930).
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Cosmology =
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Main Assumptions
- Galaxies don't impact dark matter clustering
- Number of galaxies depends on halo mass only
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- We don't know the Initial Conditions
- Data is very high dimensional
- Large number of parameters to constrain
- N-body sims extremely slow to run! (Sampling parameter space > O(10^6) calls)
Cosmology =
Galaxy =
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?
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Summarise the data
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N-body simulations
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How to emulate?
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Credit: James Hensman
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Credit: James Hensman
Optimize the marginal likelihood: Analytical solution!
Pros
- Easy to get going
- Small number of free parameters
Cons
- Scales badly with training set size O(n^3)
- Scales badly with number of input features
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Credit: https://cs231n.github.io/convolutional-networks/
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Loss Value
Weights
Weights
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+
+
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Network A
Network B
Pros
- Fast, does not scale with n
- Can model large input features
Cons
- Prone to overfitting: But ways to avoid it
- "Harder" to train (requires more exploration)
What to emulate?
- Flexibility: Vary galaxy tracers, and their cross-correlations. Marginalising over g requires flexible g!
-
1% accuracy1-sigma accuracy:- Emulator only as good as data used for training
- Simplify input/output relation through physical models
Neural Net
Analytical
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The Streaming Model
PAIRWISE VELOCITY
DISTRIBUTION
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Probability of finding a pair of galaxies at distance r
Virial motions within halos
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Infall towards halos
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On large scales,
slowly varying function of
n = 4 reproduces clustering down to small scales
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INFALL
OUTFLOW
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Two representative extensions to General Relativity:
- The background expansion is the same as LCDM
- One parameter to describe deviations from LCDM
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How do these vary with cosmological parameters on small scales?
Described by four parameters
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Code available on github soon!
Likelihood evaluations
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But... How much information are we ignoring??
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Credit: ChangHoon Hahn et al https://arxiv.org/abs/2012.02200
P
B
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r
r1
r2
r3
Credit: Sihao Cheng et al https://arxiv.org/pdf/2006.08561.pdf
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Input
x
Neural network
f
Representation
(Summary statistic)
r = f(x)
Output
o = g(r)
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Increased interpretability through structured inputs
Modelling cross-correlations
ML and cosmology
- ML to accelerate non-linear predictions: allow MCMC sampling of non-linear scales
- Precision of future surveys: what and how we emulate will have a big impact on cosmological constraints
- Can ML extract **all** the information that there is at the field-level in the non-linear regime?
- Compare data and simulations, point us to the missing pieces?
deck
By carol cuesta
deck
- 378