The document discusses using artificial neural networks (ANNs) to analyze 21cm cosmology data. Specifically, it discusses using ANNs to: 1) Emulate and speed up computation of 21cm power spectra from EoR parameters by 3 orders of magnitude. 2) Reconstruct EoR parameters like the mean free path and virial temperature from 21cm power spectra. 3) Recover the ionized bubble size distribution from 21cm power spectra to learn about the EoR source properties. 4) Generate 21cm distributions from Lyman-alpha emitter galaxy distributions using generative adversarial networks.

1. 21cm cosmology with ANN
Hayato Shimabukuro (Yunnan university,SWIFAR)

2. Contents
• Basics of 21cm signal
• Basics of artificial neural networks (ANN)
• Parameter studies
• Recover ionised bubble size distribution
• Generating 21cm distribution from LAE
• Our on-going work

3. History of the Universe
presentpast
https://universe-review.ca/
EoRDark
Ages
Recombination
Big
Bang
Dark Ages・・・ No luminous object exists. (z>~30?)
Epoch of Reionization (EoR)・・・UV photons by luminous
objects ionize neutral IGM. (z~6-15?)
Cosmic Dawn・・・First stars and galaxies form. (z~30?)

4. 21cm line
•21cm line radiation : Neutral hydrogen atom in IGM emits the
radiation due to the hyperfine structure.
z=6 → 1.5m or 202 MHz
z=20 → 4.4m or 68MHz
Radio wavelength.
We have yet to observe 21cm signal at EoR and cosmic dawn!
We can map neutral hydrogen atom in the IGM by 21cm lines.
However…

5. Red : cosmology Blue : astrophysicsTb =
TS T
1 + z
(1 exp(⌧⌫))
⇠ 27xH(1 + m)
✓
H
dvr/dr + H
◆ ✓
1
T
TS
◆ ✓
1 + z
10
0.15
⌦mh2
◆1/2 ✓
⌦bh2
0.023
◆
[mK]
Brightness temperature
21cm power spectrum (PS) : h Tb(k) Tb(k
0
)i = (2⇡)3
(k + k
0
)P21
Scale dependence
21cm line signal

6. Artificial Neural Network (ANN)
An ANN is a mathematical
model of human brain network.
ex.) Rumelhart et. al (1986)
LeCun et. al (1989)
Recently, it has been applied to
field of astronomy.

7. Artificial Neural Network (ANN)
•Training network with training
dataset, ANN can approximate any
function which associates input and
output values.
y = f(x)
• Applying trained network to unknown
data for prediction.
yANN = f(xtest)
• ANN consists of input layer, hidden
layer and output layer. Each layer has
neurons.
Non-linear regression Problem

8. Current application of the ANN to 21cm signal
•Emulator
•EoR parameter estimation
•EoR source model distinguish (Hassan et al 2019)
•others
(Li et al 2019, Chardin et al 2019, Madhurima et al 2020,
Shimabukuro et 2020, Yoshiura, HS et al 2020)
(Kern et al 2017, Schmit et al 2018,Aviad et al 2020)
(Shimabukuro et al. 2017, Nicolas et al 2019, Doussot et al 2019)

9. Emulator
EoR parameters 21cmPSANN MCMC
Before : 2.5days on 6 cores
After: 4minutes
speed up by 3 orders of magnitude
(Schmit et al 2018)
(input) (output)

10. Parameter studies
(Shimabukuro et al 2017)

11. 21cm power
spectrum
Input Output
EoR parameters
We construct neural network by 21cm power spectrum and EoR
parameters.
Inverse problem
We predict EoR parameters from 21cm power spectrum.

12. z=9, 10, 11. PS with thermal noise and cosmic variance
Reconstructed by 21cm PS at z=9,10,11
Rmfp ⇣
Tvir
10
20
30
40
50
60
10 20 30 40 50 60
Rmfp,ANN[Mpc]
Rmfp,true[Mpc]
10
20
30
40
50
60
10 20 30 40 50 60
ζANN
ζtrue
1
10
100
1 10 100
Tvir,ANN[K/10
3
]
Tvir,true[K/10
3
]
Red : z=9,10,11
Blue : z=9
EoR parameters can be reconstructed from
21cm PS well.
Shimabukuro & Semelin, 2017

13. Recover bubble size distribution
(Shimabukuro et al 2020)

14. Bubble size distribution (BSD)
''How large bubbles are distributed ?’'
Giri 2019
What can we learn from BSD?
Giri et al 2017
•EoR source (galaxy or AGN?)
•ionizing efficiency, recombination, radiative feedback.
(ex.)

15. BSD from 21cm observation
Kakiichi et al 2017
IFT
21cm Image BSD
Incomplete IFT due to limited number of antenna in interferometer.
visibility
We do not observe 21cm image directly by radio interferometer!
We first observe visibility and perform Inverse Fourier
Transformation (IFT) to obtain 21cm image. Then, compute BSD.

16. BSD from 21cm PS
Kakiichi et al 2017
21cm power spectrum BSDvisibility
We can directly compute 21cm power spectrum from visibility
without Inverse Fourier Transformation.
Can we recover BSD from 21cm PS ?
Avoid information loss by incomplete IFT.

17. 21cm power
spectrum
Input Output
ionised bubble size
distribution
Our datasets consist of 21cm power spectrum as input data and bubble
size distribution as output data.
Our strategy
We try to recover ionised bubble size distribution from 21cm PS

18. Recovered BSD
Black: Distribution obtained
by 21cm 3D image directly.
Red: Distribution obtained
by ANN.
xHI = 0.39
Shimabukuro, Mao and Tan (2020)

19. Generating 21cm distribution
from LAE galaxies with GAN
(Yoshiura, HS et al 2020)
Dr. Shintaro Yoshiura (University of Melbourne)

20. Reconstruct HI distribution
Main purpose :
Predicting the 21cm line map from the Lyman-Alpha Emitter (LAE) galaxy
distribution using Deep Learning(GAN).
Fig. 5. Same as Figure 4, but for the LAEs z = 6.6. The large red open squares indicate the LAEs with spatially extended
(Ouchi et al. 2009a) and CR7 (Sobral et al. 2015). See Shibuya et al. (2017b) for more details.
Ouchi+2017z=6.6
?
Input : LAE Output : 21cm line

21. Result
It seems that the 21cm distribution at large scales is reconstructed well.
However, it seems that reconstruction is not well at smaller scales.

22. Power spectrum
21cm power spectrum
.
.
o
n
αesc
˙Nion,int[number/yr], (4)
fesc,c, critical halo mass Mturn =1010
,
.
lanetto 2007 Zahn 2011, 21cmFAST
. R ,
,
)tage (5)
(x) R
, tage z = 15 z = 6.6
,
l(R) (6)
, Vcell . R
work is trained using ‘H-f02’ model at neutral f
ber 2 and the input is LAE of ‘H-mid’ model at
bin number 3, the output image is named “Hf02
models used in this work is listed in Table. 3.
A measure tool to study the 21cm line is the a
trum, which is given by
Pi(|k|) = (2π)2
δD(k − k′
)⟨δi(k)δ∗
i (k′
)⟩
where k is wavenumber in 2D Fourier space an
observation or the output of network. The auto
of observed data (reconstruct image) is repre
Ppix. To detect the 21cm signal from the 21
we consider the cross correlation between the
and reconstruct image, which is given as
PX (|k|) = (2π)2
δD⟨δobs(k)δ∗
pix(k′
)⟩
where δobs and δpix are fluctuation in observe
construct image, respectively. The correlatio
given as
PX (k)
Red : true
Black : output
This result indicates that the network successes to learn statistical property
of the 21cm-line fluctuations.
S. Yoshiura et al.

23. Ongoing works

24. 21cm power
spectrum
Input Output
Minkowski functionals
ANN
21cm global signal
Other applications of the ANN to 21cm signal
Recover other quantities from 21cm power spectrum
with ANN.
(Shimabukuro,Mao, Fialkov)
(Jiao,Zhaoting, Shimabukuro,Mao)

25. Summary
• The ANN constructs approximate function between
input and output.
• We recover statistical quantities from the 21cm PS
with the ANN.
• We also applied deep learning to 21cm image
prediction.

26. Bakcup

27. Pix2Pix
Image-to-Image Translation with Conditional Adversarial Networks
(Isola+2016, arXiv : 1611.07004)
Image translator (example : edge shoes to colored shoes)
Training Generator (G) and Discriminator (D) using input(x) and true(y) images.
In this first work, we use an implementation of pix2pix
(https://github.com/affinelayer/pix2pix-tensorflow)
Please see the site for details.
fake
G(x)
x
D
real
D
G
x y
x
Figure 2: Training a conditional GAN to map edges!photo. The
discriminator, D, learns to classify between fake (synthesized by
the generator) and real {edge, photo} tuples. The generator, G,
learns to fool the discriminator. Unlike an unconditional GAN,