Application of machine learning in 21cm cosmology

Machine learning approaches in 21cm cosmology
Hayato Shimabukuro(島袋隼⼠)
（Yunnan university, Nagoya university）
@Galaxy-IGM workshop (2023/7/31-8/4)

The history of the universe
©NAOJ
Dark Ages・・・No luminous object exists.
Epoch of Reionization(EoR)・・・UV photons by luminous objects ionize
neutral hydrogen in the IGM ( ).
z ∼ 6 − 15
Cosmic Dawn・・・First stars and galaxies form ( ).
z ∼ 20 − 30

The history of the universe
©NAOJ
Dark Ages・・・No luminous object exists.
Epoch of Reionization(EoR)・・・UV photons by luminous objects ionize
neutral hydrogen in the IGM ( ).
z ∼ 6 − 15
Cosmic Dawn・・・First stars and galaxies form ( ).
z ∼ 20 − 30
These epochs have not been
observed yet

21cm line emission
Proton Electron
21cm line emission(1.4GHz)
(Neutral) hydrogen atom is a good tracer for IGM through the dark ages to EoR.
singlet
Triplet
21cm radiation: neutral hydrogen atom emits 21cm line emission due to hyperfine structure.
Transition
Tb =
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
Red : cosmology Blue : astrophysics

21cm line emission
We can map the distribution of HI in the IGM with 21cm line.
Liu & Shaw (2020)
To describe 21cm signal statistically…
Redshift

21cm line emission
Liu & Shaw (2020)
21cm global signal: Sky-averaged 21cm line
signal
Redshift

Redshift
Liu & Shaw (2020)
21cm line emission

21cm line power spectrum
h Tb(k) Tb(k
0
)i = (2⇡)3
(k + k
0
)P21
Redshift
Liu & Shaw (2020)
21cm line emission

Bouman et al 2018
21cm global signal?
•In 2018, the EDGES group reported the detection of 21cm line global signal. If it’s true, this
is the first detection of the high-redshift 21cm line! But...
Singhʼs slide
The reported signal cannot be explained by standard
cosmology and astrophysics!

Bouman et al 2018
21cm global signal?
Singhʼs slide
SARAS3 did not detect signal
（Singh+2022）

Bouman et al 2018
21cm global signal?
Singhʼs slide
SARAS3 did not detect signal
（Singh+2022）
Under debate! Need exotic physics?
mis-calibration? unknown systematics?

HERA collaboration 2022b
Astrophysics from 21cm upper limits
•We obtained some constraints on astrophysical
parameters from 21cm power spectrum upper limits.
•HERA firstly constrains X-ray parameters at high
redshift.
Shimabukuro+ (2023)

redshift.

redshift.
•High redshift galaxies suggest higher X-ray luminosity
and lower metallicity than local galaxies.

redshift.
•High redshift galaxies suggest higher X-ray luminosity
and lower metallicity than local galaxies.
Astrophysics with 21cm line signal is
around the corner!?

•The construction started in 2022
•The observation is going to start in 2027

The Japanese SKA EoR team is always
waiting for your participation!
•The construction started in 2022
•The observation is going to start in 2027

FARSIDE
Lunar Crater Telescope
“We choose to go to the moon”
-J.F. Kennedy(1962)
Go to the moon・・・
鸿蒙计划
•Is radio astronomy in the 2030s and 2040s the era of 'Lunar Radio
Astronomy' using lunar telescopes and lunar orbiting satellites?
•On the Moon, the effects of the ionosphere and RFI, which are
disturbing for low-frequency radio observations, can be suppressed.
•The dark ages can be used for pure cosmological exploration.

Applications of machine
learning(ML)

Application of ML to astronomy
Hey, ChatGPT! Tell me about the application of the ML in the context of EoR and 21cm studies.

Application of ML to astronomy
Hey, ChatGPT! Tell me about the application of the ML in the context of EoR and 21cm studies.
何か、ふんわりと正しい。。。

•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(test data) for prediction.
yANN = f(xtest)
• ANN consists of input layer, hidden
layer and output layer. Each layer has
neurons.
nonlinear regression Problem
Artificial Neural Network (ANN)
https://www.snexplores.org/article/explainer-what-is-a-neuron

•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(test data) for prediction.
yANN = f(xtest)
• ANN consists of input layer, hidden
layer and output layer. Each layer has
neurons.
nonlinear regression Problem
Artificial Neural Network (ANN)

•Emulator + MCMC →parameter estimate
•Direct parameter estimate
•Distinguish EoR sources
(e.g) Hassan+ (2019)
•Others
(e.g.) Mertens+ (2018,2020), Li+ (2019), Chardin+ (2019), Yoshiura+ (2020), Shimabukuro+
(2022), Bianco+ (2021,2023)
(e.g.) Kern+ (2017), Schmit+ (2018), Aviad+ (2020), Bevins+ (2021), Yoshiura+ (2023)
(e.g.) Shimabukuro&Semelin (2017), Gilet+ (2018), Nicolas+ (2019), Doussot+ (2019),
Choudhury+(2020,2021,2022), Zhao+ (2022a,b), Vivekanand+ (2023)
21cm study + ML

Statistical challenge in 21cm cosmology
Cosmology

Cosmology 21cm cosmology

Cosmology 21cm cosmology
We can learn astrophysics if EoR
parameters are constrained.

Traditional approach
EoR parameters 21cm power spectrum
Semi-numerical
Simulation (e.g.
21cmFAST)
Likelihood calculation
MCMC(Markov Chain Monte Carlo)
Obtain posterior for parameters
•For likelihood calculation, we need to perform
a simulation for every parameter.
It takes too much time for MCMC!
(input) (output)
Schmit+ (2018)

EoR parameters 21cm power spectrum
Likelihood calculation
Obtain posterior for parameters
•We construct the ANN which can associate
parameters with 21cm power spectrum.
•We directly calculate the 21cm power
spectrum from parameters. It can bypass to
conduct simulations.
Emulator
MCMC(Markov Chain Monte Carlo)
(input) (output)
Schmit+ (2018)

EoR parameters 21cmPS MCMC
w/o emulator : 2.5days on 6 cores
w/ emulator: 4 minutes
Schmit+ (2018)
(input) (output)
speed up by 3 orders of magnitude
Emulator

Parameter estimate (inverse problem)
(input)
21cmPS
(output)
EoR parameters
10
20
30
40
50
60
10 20 30 40 50 60
R
mfp,ANN
[Mpc]
Rmfp,true[Mpc]
10
20
30
40
50
60
10 20 30 40 50 60
ζ
ANN
ζtrue
1
10
100
1 10 100
T
vir,ANN
[K/10
3
]
Tvir,true[K/103
]
(Shimabukuro &
Semelin 2017)
Input : 21cm PS + thermal noise(SKA)

Parameter estimate (inverse problem)
(input)
21cmPS
(output)
EoR parameters
10
20
30
40
50
60
10 20 30 40 50 60
R
mfp,ANN
[Mpc]
Rmfp,true[Mpc]
10
20
30
40
50
60
10 20 30 40 50 60
ζ
ANN
ζtrue
1
10
100
1 10 100
T
vir,ANN
[K/10
3
]
Tvir,true[K/103
]
(Shimabukuro &
Semelin 2017)
Input : 21cm PS + thermal noise(SKA)
(Choudhury+2022)
Input : 21cm PS +
Foreground + thermal
noise(SKA)

parameters
21cm light-cone CNN
(input) (output)
Image > Parameters
(Gillet+ 2018)

Posterior inference with machine learning
•We usually DO NOT evaluate the uncertainty of machine learning itself. ANN just returns “points”.
p(θ|t0) ∝ ℒ(t0 |θ)p(θ)
•In MCMC, we obtain the posterior of parameters and we need likelihood (and prior) to perform
MCMC.
Likelihood
Prior
Posterior
•We sample various parameter values and iterate the
calculation again and again in the MCMC, while the ANN
returns 1 point for parameter sets.

(Zhao+ 2022a)
•Zhao+ (2022) suggested a “likelihood-free” approach (DELFI, Density estimation likelihood-
free inference) or simulation-based inference in 21cm study. They consider conditional density
distribution instead of likelihood.
p(θ|t0) ∝ ℒ(t0 |θ)p(θ)
See also Prelogovic & Mesinger(2023)

Data: 21cm image
CNN(compressor) > EoR parameters(Summaries)
(Zhao+ 2022a)
CNN as a compressor
Parameters, θ
21cm image maps are generated
from parameters by semi-numerical
simulation
CNN compresses 21cm image map into
summary statistics. (See also Sui+ 2023)

(Zhao+ 2022a)
•Mixture density networks(MDN) (Bishop 1994)
•Masked Autoencoder for Density Estimation (MADE) (Papamakarios+ 2017)
(See also Alsing+2019)
MCMC sampling
Training dataset {θ, t}
We train neural networks with and obtain conditional density with simulations.
{θ, t} p(t ∣ θ)

(Zhao+ 2022a)
•Mixture density networks(MDN) (Bishop 1994)
•Masked Autoencoder for Density Estimation (MADE) (Papamakarios+ 2017)
(See also Alsing+2019)
MCMC sampling
Training dataset {θ, t}
We obtain the
probability distribution
We train neural networks with and obtain conditional density with simulations.
{θ, t} p(t ∣ θ)

Parameter inference with error bars
(Zhao+ 2022a)
•We can put error bars on obtained parameters with DELFI. (c.f.) CNN
EoR parameters( )
with posterior
ζ, Tvir
(Gillet +2018)

Parameter inference with error bars
(Zhao+ 2022a)
•We can put error bars on obtained parameters with DELFI. (c.f.) CNN
EoR parameters( )
with posterior
ζ, Tvir
(Gillet +2018)
We cannot obtain
posterior by CNN only.

(Zhao+ 2022a)
•We can directly compare the posterior obtained from 21cm image map by CNN with the posterior
obtained from 21cm PS with MCMC.
Posterior from 21cm image and PS
21cm image map can provide tighter constraints on EoR parameters than 21cm PS

(Zhao+ 2022b)
•We can also compare the posterior obtained from 21cm PS by MCMC with posterior obtained by
machine learning based approach (DELFI).
•The posterior probability distribution can be obtained with the same accuracy when MCMC is performed
and when DELFI is applied.
Comparing posteriors

Recovering statistics from another statistics
•We can associate statistics with other statistics by the ANN. Can we recover statistics from
another statistics by the ANN?
Statistics A Statistics B

21cm power spectrum

21cm power spectrum Bubble size distribution
(BSD)

21cm power spectrum
Bubble size distribution
(BSD)
(Note) It does not mean 21cm PS contains beyond Gaussian information. Training enables us
to connect a data space to another data space.
Data space Data space

Recovering BSD from 21cm PS
HS, Mao, Tan (2022)

Reconstruction of HI distribution from LAE
map is marked in angles (degrees) and the projected distances (comoving megaparsecs).
Fig. 5. Same as Figure 4, but for the LAEs z = 6.6. The large red open squares indicate the LAEs with spatially extended Lyα emission including Himiko
(Ouchi et al. 2009a) and CR7 (Sobral et al. 2015). See Shibuya et al. (2017b) for more details.
Input :
Lyman-alpha emitter galaxies
Output :
HI distribution
Yoshiura, HS+ (2021)
cGAN
Shintaro Yoshiura (NAOJ)

Foreground problem
Chapman & Jelic (2019)
•The 21cm line signal is buried in very intense foreground radiation (e.g. Galactic foregrounds).
Foreground: ~ a few-10 K
21cm signal: ~ a few-10 mK
3 - 4 order!
Very challenging issue!
Suggestions
•Foreground removal
•Foreground avoidance

Gaussian Process (GP)
https://yuyumoyuyu.com/2021/03/07/gaussianprocessregression/

Foreground removal with GP
•Recently, Gaussian Process Regression (GPR) is employed ion LOFAR (Mertens+ 2018,2020)
d = ffg + f21 + n d ∼ N(m(ν), K(ν, ν))
The probability distribution is assumed to be expressed
by Gaussian, which is characterized by
covariance(and mean).
Joint probability distribution
Remove foreground
K = Kfg + K21 + Knoise
E (f′

fg) = m (ν′

) + K (ν′

, ν) [K(ν, ν) + σ2
n I]
−1
(d − m (ν′

))
cov (f′

fg) = K (ν′

, ν′

) − K (ν′

, ν) [K(ν, ν) + σ2
n I]
−1
K (ν, ν′

)
dres = d − E (ffg)

Foreground removal with ML
Remove foreground
(Hothi+ 2020)
Hothi+ (2020) reported GPR has better performance than GMCA and FastICA for
foreground removal (simulated sky).

Application of machine learning in 21cm cosmology

21cm cosmology + machine learning
has big potential!

Our review paper
Shimabukuro+(2023)
PASJ

メンバー募集中！
天⽂学会前⽇!
興味のある⼈は声をかけて
ください！

HERA collaborations 2022
•10h observation data.
•Foreground avoidance.
•Largely consistent with
thermal noise.
Current upper limits on 21cmPS

Saxena+ (2022)
Fornasini+ (2020)

Bishop (1994)
Bishop (1994)
p(t ∣ x) =
m
∑
i=1
αi(x)ϕi(t ∣ x)

What summary statistics is better?
Sui+ (2023)
Wavelet scatter transformation is better summary statistics
I(x; y) = KL(p(x, y)∥p(x)p(y))
=
𝔼
p(x,y) [
log
p(x, y)
p(x)p(y) ]
Evaluating summary statistics by mutual information

EoR sourcs
21cm map ANN
(input) (output)
Distinguish EoR sources
Hassan +2019

''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.)
Bubble size distribution(BSD)

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.

Kakiichi+ (2017)
21cm power spectrum BSD
visibility
We can directly compute 21cm power spectrum from visibility without Inverse Fourier
Transformation.
Avoid information loss by incomplete IFT.

Kakiichi+ (2017)
21cm power spectrum BSD
visibility
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.

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

Recovered BSD
Black: Distribution obtained by
21cm 3D image directly.
Red: Distribution obtained by
ANN.
53

Different stage of reionization
54

Effect of thermal noise
55
21cm PS with thermal noises
(SKA level)
Errors are estimated by 10
realizations thermal noises

Accuracy for all test data
Relative error between two size
distributions at fixed bubble
radius for all test data.
Good recovery for all test data.
57

Red: 21cm power spectrum > ANN > bubble size distribution
Blue: 21cm power spectrum > MCMC > parameter > bubble size distribution
21cm PS > parameter > BSD

Algorithm for calculating bubble size distribution
2. Generating density field
3. Generating ionization field from density field with excursion-set formalism for modeling Reionization
1.Input EoR & cosmological parameters
21cmFAST
Roughly speaking, it evaluates whether isolated region is
ionized or not (Furlanetto+2004, Zahn+ 2010).
4. Evaluating ionized bubble size distribution
(Zahn+2007, Mesinger & Furlanetto 2007, See also Giri+ 2018)
•Randomly choose a pixel of ionized region.
•Record the distance from that pixel to neutral
region along randomly chosen direction.
•Repeat Monte Carlo procedure times.
107
Ionized region
R
Neutral region

• 1000 EoR models
• 48000 training datasets (20% of which is used for validation)
• 2000 test datasets
• 21cm PS is ranged from k=0.11/Mpc to 1.1/Mpc with 14 bins
• 5 hidden layers
• 212 neurons at each hidden layer
• 2000 iterations
Setup

Evaluate accuracy: noise
We evaluate accuracy of obtained parameters by chi-square. Smaller
chi-square means better accuracy.
single z
As expected, accuracy becomes worse if we add noise to 21cm
power spectrum.
without noise with noise

Evaluate accuracy: redshift
We evaluate accuracy of obtained parameters by chi-square. Smaller
chi-square means better accuracy.
multiple z
The accuracy of parameter estimation is improved when we
consider redshift evolution of 21cm power spectrum.
Single z
Both include noise

Application of machine learning in 21cm cosmology

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