Recovering HII bubble size
distribution with artificial neuralnetwork
Hayato Shimabukuro (Tsinghua University)with Yi Mao21cm power spectrum
We first aim to detect 21cm signal statistically.
03021cm power spectrum (PS) : h Tb (k) Tb (k )i = (2⇡) (k + k )P21(We use 21cmFAST)

Scale dependence

Redshift dependence

WF
effectX-ray
heatingEoR

Pober et al (2014)z

Distinguish EoR models
We often discuss distinguishing EoR models on the basis of 21cm
power spectrum. (e.g. EoR parameters, feedback, ionising sources)
Dixon et al.(2016)

LB1: only high mass halo M>10ˆ9 M_sun
LB2: including low mass (10ˆ8-10ˆ9 M_sun)
LB3: including low mass with radiative feedback
LB4: same with LB3 but mass dependent FB

Bubble size distribution (BSD)HII bubble size distribution is another method to break degeneracy in
EoR models.

However!!

Difficult to determine bubble size and measure BSD.
Some methods are suggested to measure BSD from ionised map•Mean free path

•Friend-of-Friend (FoF)

Mesinger & Furlanetto (2007)

Friedrich+ (2011)•Spherical average method•WatershedZahn+ (2007)

Lin+ (2016)

BSD from 21cm tomography
We practically measure BSD from 21cm tomography data.
Different from the case of measuring BSD from ionisation map.
•ionised map•21cm mapbinary map (ionized or neutral)

Not binary map

Therefore,
we need to transform 21cm map into binary map (ionized or neutral).
We need to fix threshold to distinguish fields.
It is difficult because 21cm map depends on both x, δMaking binary map
Giri+ 2017
Giri+ 2017 focuses on the fact that 21cm PDF is bimodal.
•K-means methodunsupervised learning algorithm for clustering problem

BSD for different sources
Giri et al 2017

MFP-BSDNo smoothingsmoothingOur strategy

Input

Output21cm powerspectrum

HII size distribution

Our datasets consist of 21cm power spectrum as input data andbubble size distribution as output data.

Artificial Neural Network (ANN)• ANN consists of input layer, hidden
layer and output layer. Each layer has
neurons.
•Training network with training
dataset, ANN can approximate any
function which associates input andoutput values.

y = f (x)• Applying trained network to unknown
data in order to obtain expected value.

yANN = f (xtest )Motivation•

Some previous studies measure HII size distribution from21cm 3D map directly.

•

From observational aspect, we require good angularresolution to make 21cm map.

•

Therefore, I attempt to recover HII size distribution from21cm PS that does not require making 21cm map.

Setup•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 14bins•

5 hidden layers•

212 neurons at each hidden layer

Recovered BSD
Black: Distribution obtainedby 21cm map directly

xHI = 0.39

Red: Distribution obtained
by ANN

Using 21cm PS at
0.1<k[/Mpc]<1

Different epoch of reionization

Scale dependence

21cm PS
kmin < k < 1.1Mpc

1

Scale dependence

Thermal noise
21cm PS with thermal
noises (SKA level)
Errors are estimatedby 10 realizations
thermal noises

Thermal noiseOther ideas?

Input
21cm powerspectrum

Outputbubble size distribution
Escape fraction
global signalMinkowski functionals

Summary•

We applied artificial neural networks (ANN) to analysis of21cm signal.

•Reconstructed EoR parameters and HII size distribution aregood agreement with true values.

•(Future work) Are there other 21cm observables which we
can apply machine learning to ?

19

Non-Gaussianity of 21cm fluctuations
21cm PS analysis is useful, but it is imperfect to describe 21cm
fluctuations.
21cm-PDF is highly non-Gaussian owing to astrophysical effects.
Giri et al 2018

Higher order statistics !

21cm PDF is bimodal

Bispectrum
HS+ 2016, Watkinson+ 2017,Majumdar+ 2018
Skewness
HS+2015, Kubota + 2016

Morphology of ionised bubble
Kulkarni et al 2017

AGNGalaxyK-means method
Giri+ 2017
Giri+ 2017 focuses on the fact that 21cm PDF is bimodal.
•K-means method
unsupervised learning algorithm for clustering problem

Comparison of methods
Yin+ (2016)

See solid line
Black : Reference
Green : Watershed (WS)Blue : Mean free path (MFP)
Red : Spherical average (SA)WS and MFP seem better

Different models

What does k_min give best accuracy?

Training accuracy

HII bubble size distribution
Black: Distribution obtainedby 21cm map

Red: Distribution obtained by ANN

21cm PS at
0.1<k[/Mpc]<1

Recovered BSD
xHI = 0.39

Black: Distribution obtainedby 21cm map directly
Red: Distribution obtained by ANN

Using 21cm PS at
0.1<k[/Mpc]<1