# Dust Extinction Measures for $z\sim 8$ Galaxies using Machine Learning on
JWST Imaging

Kwan Lin Kristy Fu,1 Christopher J. Conselice,1 Leonardo Ferreira,2 Thomas
Harvey,1 Qiao Duan,1 Nathan Adams,1 Duncan Austin1
1Jodrell Bank Centre for Astrophysics, University of Manchester, Oxford Road,
Manchester, UK
2 School of Physics and Astronomy, University of Victoria, Victoria, BC,
Canada E-mail<EMAIL_ADDRESS>(KTS)

(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

We present the results of a machine learning study to measure the dust content
of galaxies observed with JWST at z > 6 through the use of trained neural
networks based on high-resolution IllustrisTNG simulations. Dust is an
important unknown in the evolution and observability of distant galaxies and
is degenerate with other stellar population features through spectral energy
fitting. As such, we develop and test a new SED-independent machine learning
method to predict dust attenuation and sSFR of high redshift (z > 6) galaxies.
Simulated galaxies were constructed using the IllustrisTNG model, with a
variety of dust contents parameterized by E(B-V) and A(V) values, then used to
train Convolutional Neural Network (CNN) models using supervised learning
through a regression model. We demonstrate that within the context of these
simulations, our single and multi-band models are able to predict dust content
of distant galaxies to within a 1$\sigma$ dispersion of A(V) $\sim 0.1$.
Applied to spectroscopically confirmed z > 6 galaxies from the JADES and CEERS
programs, our models predicted attenuation values of A(V) < 0.7 for all
systems, with a low average (A(V) = 0.28). Our CNN predictions show larger
dust attenuation but lower amounts of star formation compared to SED fitted
values. Both results show that distant galaxies with confirmed spectroscopy
are not extremely dusty, although this sample is potentially significantly
biased. We discuss these issues and present ideas on how to accurately measure
dust features at the highest redshifts using a combination of machine learning
and SED fitting.

###### keywords:

keyword1 – keyword2 – keyword3

††pubyear: 2022††pagerange: Dust Extinction Measures for $z\sim 8$ Galaxies
using Machine Learning on JWST Imaging–Dust Extinction Measures for $z\sim 8$
Galaxies using Machine Learning on JWST Imaging

##  1 Introduction

Interstellar dust represents potentially a significant unknown in observing
early galaxies in optical and near-infrared wavelengths (e.g., Casey et al.,
2014; Fudamoto et al., 2020). Due to dust effects, such as extinction and the
scattering of light, images of early galaxies are often obscured, and
properties such as dust composition (Calzetti et al., 1994; Min et al., 2006;
Spoon et al., 2006; Dwek et al., 2014), AGN (Treister et al., 2010), and
metallicity (Shivaei et al., 2020) can affect spectral energy distribution
modelling accuracy (e.g., Juodžbalis et al., 2023). On the other hand, solid
measurements of the dust content or reddening can help build accurate models
of galaxies, and are important in our understanding of galaxy evolution. We
are now in a position, with ALMA and JWST, to learn more about dust in the
early universe and how dust affects the output of light from early galaxies.
However, there remains a significant amount we do not yet understand about
dust in the early universe, in part due to the difficulties of observing this
feature within faint high-redshift galaxies in the absence of rest-frame far-
IR light. New approaches and ideas are needed to trace this aspect in the
early universe.

Observations starting from IRAS and COBE in 1980s and 90s and leading into
JCMT/SCUBA, SMO, and ALMA, among others, have identified many high-redshift
galaxies which are faint or invisible in the optical but bright in the far-
IR/sub mm (e.g., Casey et al., 2014; Hodge & da Cunha, 2020; Dayal et al.,
2022). These galaxies are sometimes known as Dusty Star-Forming Galaxies
(DSFGs) due to being enshrouded in dust, which obscures observations at
optical and UV wavelengths. Observed DSFGs are generally massive,
ultraluminous, and have high Star Formation Rates (SFRs) (Hodge et al., 2013).
DSFGs include sub-millimeter galaxies (SMGs), systems observed to be the
brightest systems at 850 $\mu$m but are incredibly faint in other bandwidths
(Blain et al., 2002). High-z SMGs are important as they are thought to
contribute significantly to the SFR and energy in this time period, where the
average SFR is $\sim$ 200-300 and can reach 1000 $M_{\bigodot}\textup{
yr}^{-1}$ (e.g., Blain et al., 2002; Daddi et al., 2005), making up a
significant portion of SFR in this time period (Chapman et al., 2005). Large
amounts of stellar light heats up the dusty star forming environment which
become extremely bright in the infrared. This can impact measurements as high
dust temperatures increase the sub-mm observed flux by up to a factor of 10
(Blain et al., 2002; Eales et al., 1999), causing an overestimation of the
number density of high-z galaxies (Hodge & da Cunha, 2020). These are,
however, for the most part extreme and relatively rare systems and the effects
of dust on more typical galaxies is harder to know for certain.

Aside from energetic, high star-forming galaxies, dust is also important in
understanding how it affects observations of galaxies, including their
measured stellar masses and star formation rates, among other properties. For
example, Fudamoto et al. (2017) suggests that there is an evolution in the
dust attenuation curve between z $\sim$ 3 to 6 that produces observable
effects. Remarkably, ALMA shows that even UV bright galaxies, whose light
would not normally be thought to be attenuated much by dust, often have their
star formation dominated by dust emission at $z\sim 7$ (e.g., Dayal et al.,
2022; Inami et al., 2022). It is thus important to learn more about the dust
content at high redshifts to accurately constrain the properties of distant
galaxies, such as ongoing and past star formation, metallicity, and with
spectral fits of SED properties based on their spectral energy distribution.

Another reason for this is a full accounting of galaxy formation. One aspect
of this is measuring the star formation history of galaxies. Measurements of
cosmic star formation rate density (SFRD) has been shown to reach a peak at z
$\sim$ 2 (Juneau et al., 2005; Madau & Dickinson, 2014) with SFR dropping off
at either ends of the peak, but there may still be significant amounts of star
formation at very high redshifts z > 8 (Ellis et al., 2012; Robertson et al.,
2015; Duncan et al., 2014; Adams et al., 2023). For example, Daddi et al.
(2009) suggests that a significant percent of SMGs are located at z > 6,
indicating that dust clouds were well enriched before this time period for
star formation, showing the importance of SMGs in early cosmic SFRD. Recent
observations using ALMA and JWST at redshifts $\geq$ 5 (Blain et al., 2002;
Coe et al., 2012; Oesch et al., 2015; Naidu et al., 2022; Adams et al., 2023;
Bowler et al., 2023) show that dust may still be an important aspect even back
to the very first galaxies, yet it has proven difficult to constrain this.

Other studies utilising the HST (Bouwens et al., 2007; Dunlop, 2011; Wilkins
et al., 2011; Robertson et al., 2015) find significant amounts of dust
attenuation and evolution of dust at higher redshifts. ALMA has allowed for a
more extensive look into the dust content of these high redshift galaxies.
Laporte et al. (2017) measures the physical properties of a z = 8.38 galaxy,
finding a star formation rate of $\sim$ 20 M⊙ year-1 and dust extinction value
of $A_{V}$ = 0.74. Other ALMA studies of dust content in high redshift
galaxies (e.g., Watson et al., 2015; Hodge & da Cunha, 2020; Casey et al.,
2019; Bowler et al., 2023) find a wide range of dust extinction values, up to
$A_{V}$ = 5.64. Using the REBELS ALMA program Bowler et al. (2023) determined
through stacking galaxies that distant galaxies at $z=4-8$ show significant
dust extinction. This wide range of galaxy properties show the need for more
data in this regime to understand better how to quantify the amount and impact
of dust without requiring deep sub-mm observations, such as with ALMA, which
is all but impossible to measure for many very high redshift galaxies.

There is however some lack of consensus about the amount of dust-obscured star
formation. Casey et al. (2014); Inami et al. (2022); Barrufet et al. (2023)
estimates significant amounts of dust-obscured star formation at z > 6,
whereas other studies suggest otherwise (Zavala et al., 2021; Algera et al.,
2022). Observations of high redshift galaxies still presents many difficulties
and are constrained by technical limitations. New instruments such as JWST can
potentially allow for more information on the dust attenuation evolution in
high-redshift environments. Papers such as Faisst & Morishita (2024); Ferrara
et al. (2023); Palla et al. (2023); Ziparo et al. (2023) investigate and
constrain dust attenuation from JWST observations, also showing that high-
redshift galaxies from JWST may be bluer than previously thought (Cullen et
al., 2023; Markov et al., 2024), implying that dust is not a significant
presence within these early galaxies. Limitations and degeneracies in SED
fitting techniques also make it difficult to accurately measure dust content
without extensive data at mid and far infrared wavelengths.

We thus turn to machine learning (ML) techniques to determine the amount of
dust extinction in high redshift galaxies. Instruments such as JWST promise to
deliver higher fidelity images and see further back to earlier galaxies,
allowing us to observe and study galaxies in their infancy. In recent years,
the development of ML algorithms has made them easier and more adaptive to
learn and utilise. ML is potentially capable of using complex physical models
to extract physical parameters such as the dust extinction and sSFR of high
redshift galaxies. In the context of astrophysics, we have seen the
application of ML in uses such as galaxy classification (e.g., Hocking et al.,
2017; Cheng et al., 2020), planetary atmospheres (Hayes et al., 2020), light
curves (Tarsitano et al., 2022), and quantifying morphology (Tohill et al.,
2020).

This paper uses deep learning to pick out galaxy features that the human eye
cannot identify (as opposed to galaxy classification), and uses the power of
neural networks to predict properties for high redshift galaxies. We focus our
attempts on using features from the morphology of high-redshift galaxies to
determine if ML algorithms can take advantage of the detailed images that JWST
offers. As galactic structure can depend on observed wavelength Kuchinski et
al. (2000); Mager et al. (2018), the difference in the morphology between JWST
wavelengths could provide a way to estimate dust effects and other properties
of high-redshift galaxies.

In this paper we discuss our use of convolutional neural networks (CNN), a
type of machine learning algorithm, to estimate the colour excess and total
extinction values of high-redshift galaxies, and our attempts in applying the
CNN model onto JWST data. The outline of this paper is as follows: Section 2
gives an overview into the data and algorithm that we use, while Section 3
shows the results on both simulated as well as high-redshift galaxy candidates
from newly released JWST data. Finally, a discussion of the results in Section
4, possible improvements and future direction in the conclusion. Throughout
this paper we use the Planck cosmology.

##  2 Data and Methods

###  2.1 Simulated Data

Figure 1: SFR and MStellar of our simulated galaxies :  Values of Log SFR against Log MStellar of the Illustris TNG simulated galaxies we use within this paper. The colour of the points represent the value of the redshift for each galaxy. Simulated galaxies we use from Illustris are found at redshifts between 6 < z < 8\. Redshifts values are discrete and are noted in the legend with different colors and markers. There is a linear relationship between these two properties. At the same SFR, younger galaxies appear to have a larger LogMStellar value than the older galaxies. ID | F277W | F356W | F444W | F560W | F770W | F1000W
---|---|---|---|---|---|---
8_2405 |  |  |  |  |  |
9_3842 |  |  |  |  |  |
10_6345 |  |  |  |  |  |
11_384 |  |  |  |  |  |
12_14814 |  |  |  |  |  |
13_3717 |  |  |  |  |  |
Figure 2: Simulated Images: A selection of IllustrisTNG images used to train
the CNNs. Each galaxy is identified by its ID and is simulated in both NIRcam
and MIRI wavelengths. Images here are shown with a dust to metal ratio of 0.1
and in the same orientation. MIRI band images show much more noise and can
make it difficult to identify features from galaxies as compared to NIRcam
bands.

The simulated images we use in this paper are generated from the IllustrisTNG
TNG50-1 simulation Vogelsberger et al. (2020); Marinacci et al. (2018); Naiman
et al. (2018); Nelson et al. (2017, 2019); Pillepich et al. (2017); Springel
et al. (2017) forward modelled with the SKIRT radiative transfer code. This
ensures that we are simulating how these galaxies would appear when observed
in different JWST filters with the Near-Infrared Camera (NIRCam) and Mid-
Infrared Instrument (MIRI).

We generate this mock imaging dataset using the methods outlined in Ferreira
et al. (2022). Here we give a brief description of the process. First, all the
galaxies between redshifts z $\sim$ 6 to 8 with stellar masses above
$M_{*}>10^{8}M_{\odot}$ are selected from TNG50-1. From these, all the stellar
particles and gas cells in a region centered in the galaxy extending out to a
$60$ kpc field of view are used.

Second, as dust is not directly embedded in the simulations, we model it from
the dense cold gas assuming a dust-to-metal ratio (Camps et al., 2016;
Rodriguez-Gomez et al., 2019). Instead of using a fixed dust-to-metal ratio as
in Ferreira et al. (2022), we generate different realizations of the same
galaxies with dust-to-metal ratios varying from $0$ to $1$ in $0.1$ bins.
SKIRT uses the dust distribution to generate a dust screen that will impact
the final SED and morphology of the galaxy with the associated reddening and
extinction based on the optical depth of the dust.

Third, the stellar particles, the gas cells and dust distribution are given as
input to SKIRT. SKIRT is set-up to generate IFU datacubes in four different
orientations aligned with the simulation axes (xy, xz, yz, and an octant view)
ranging from the rest-frame UV to the far infrared. Finally, these datacubes
are processed into broadband images based on the filter response curves for
NIRCam and MIRI at the observed frame of the source redshift, as well as an
integrated spectra for each orientation.

All of these simulations were run with standard cosmology parameters from the
Planck Collaboration et al. (2016). Smaller image sizes help reduce memory
requirements and increase computational speed, so images were cropped to 32
$\times$ 32 sized arrays centered on the target galaxy before training. Each
image is normalized to prevent effects of differing fluxes in different
galaxies. Properties of the simulated galaxies include color indices, dust
attenuation, dust mass ($M_{dust}$), gas mass ($M_{gas}$), and star formation
rate (SFR). A sample of the simulated images we use within this paper are
shown in Figure 2 within six JWST broad-band filters. The simulated images
show both NIRcam and MIRI wavelengths, but only the NIRcam (F277W, F356W,
F44W) bands are used in this project. This reduced the number of parameters in
the machine, helping speed up training time and reducing the memory required.
Figure 1 shows the properties LogSFR and LogMStellar of the simulated galaxies
with the colour showing the redshift of each system. There appears to be a
linear relationship between the two values, consistent with a main sequence of
star formation. From this we can see that our systems are dominated by star
formation and no systems have becoming ’passive’ or quenched since their
formation.

###  2.2 Dust Formalism

Our primary goal in this project is to retrieve the physical parameters: dust
extinction ($A_{V}$), colour excess ($E(B-V)$) and specific star formation
rate (sSFR). Using dust extinction and colour excess, we calculate the
$R$-value by using the relation :

$R_{V}=\frac{A_{V}}{E(B-V)}$ (1)

This equation can be rewritten to calculate the dust extinction at any
wavelength $\lambda$ as given by:

${A_{\lambda}=k(\lambda)\times E(B-V)=\frac{k(\lambda)A_{V}}{R_{V}}},$ (2)

where the value $k(\lambda)$ is the reddening curve. The value of RV is
thought to be more or less constant within single galaxies, with values of
R${}_{V}=3.1$ for the Milky Way, R${}_{V}\sim 2.7$ for the SMC, and for the
Calzetti law R${}_{V}=4.05$ (Calzetti et al., 1994; Fitzpatrick, 1999). Figure
3 shows the colour excess against the total extinction, whereby both values
used to calculate the R-value. In this simulated dataset, the median of the
R-value for the simulated galaxies is $\sim$ 7, comparatively higher than the
median R-value of galaxies such as the Milky Way, which has a R-value of
around 3 (Fitzpatrick, 1999). Since the dust-to-metal (DTM) ratios that we use
to generate the simulated images varies from 0 to 1, we expect this to have an
impact on the extinction values. To breakdown the effect of various DTM values
to the high R-values, we use contour plots in Figure 3 to show the scatter of
low DTM and high DTM. The contour plot shows the density of the scatter at 10,
50 and 95% of the points. The orange contour around DTM=0.1 values shows that
the majority of R-values of the DTM=0.1 points has a similar R-value as
Calzetti et al. (1994). This can be contrasted to the green contour around the
values of DTM=0.9, which shows a much larger scatter and deviates away from
the R-values we would expect. The number of galaxies with DTM=0.1 to DTM=0.9
is roughly 9:1, thus most systems are within the range of the Calzetti dust
law.

Figure 3:  Plot of R values: Scatterplot of the simulated AV and $E(B-V)$ values from the Illustris images, used to calculated a set of R values for training by using Eq 1. In this set of simulated data, the red line shows the median value of the calculated R-value and can be compared to the three blue lines representing the average R-values from MW, SMC and Calzetti respectively (Calzetti, 2001). The points in the plot are color-mapped to the dust to metal ratio (DTM) value used to generate the images. Images with high DTM ratios have larger R-values, shown by using density contours over the points. The orange contour encircles a proportion of the dust values which have DTM=0.1, while the green contour shows the density of points using DTM=0.9. F277W | F356W | F444W
---|---|---
|  |
|  |
|  |
|  |
|  |
|  |
Figure 4: JWST Images :  A sample of galaxies taken by JWST showing the F277W,
F356W and F444W filter images used to test the CNN models. Galaxy samples are
taken from the CEERS and JADES data release, specifically of z > 6.

###  2.3 JWST Data

We use JWST data to test our results and to determine how well our calibrated
machine agrees with different methods for finding dust content values, whether
that be the $E(B-V)$ or $A_{V}$ measurements. The imaging and spectroscopic
data we use to do this test come from the CEERS survey ID: 1345, PI: S.
Finkelstein, see also (Finkelstein et al., 2022, 2023). The CEERS field
imaging consists of 9 NIRCam pointings with 7 photometric bands (F115W, F150W,
F200W, F277W, F356W, F410M and F444W). We also only use galaxies in this
analysis which have confirmed NIRSpec spectroscopic redshifts and spectra
within the JADES and CEERS fields, which we have described and analysed in
detail in Duan et al. (2023).

In this paper we utilise our own bespoke reduction of the imaging data from
the Cosmic Evolution Early Release Science Survey in the Extended Groth Strip
field (EGS). We have reduced this data independently ourselves using a custom
set-up of the JWST pipeline version 1.6.2 using the on-flight calibration
files available through the CDRS 0942. An extensive description of this
process and the resulting data quality in provided in Ferreira et al. (2023);
Adams et al. (2023).

Discrepancy between training data and testing data, known as dataset shift,
potentially weakens the capability of generalisation of our machine learning
model. Testing our machine on JWST data helps determine how well it can
generalise to other data, exposing issues in overfitting but also showing if
models trained on simulated data can be applied to observed data. The sample
of galaxies is taken from systems that are spectroscopically confirmed at
$z\sim 7$. We compare our predictions to SED fitted values using Bagpipes from
Adams et al. (2023) and Harvey et al. (2024). Below we give a more detailed
description of the data sets from which the imaging we use is taken from. A
further description of this data is presented in Duan et al. (2023).

####  2.3.1 CEERS NIRCam Imaging

Imaging we use from the CEERS (CEERS; ID=1345) NIRCam imaging (Bagley et al.,
2023) includes data across the filters: F115W, F150W, F200W, F277W, F356W,
F410M, and F444W. These data have a $5\sigma$ depth of around 28.6 AB
magnitudes within 0.1 arcsec circular apertures (Adams et al., 2023). The data
we analyse was collected during June 2022, accounting for 40% of the total
NIRCam area coverage.

We use our own bespoke reduction of this data using a custom set-up of the
JWST pipeline version 1.6.2 using the in-flight photometric zero-point
calibration files available through the CDRS 0942. We provide an extensive
description of this process and the resulting data quality in Adams et al.
(2022); Adams et al. (2023).

In addition to this, we use the v1.9 EGcS mosaics HST data from the CEERS
team, processed using the methodologies outlined in Koekemoer et al. (2011).
This notably includes enhancements in calibration and astrometric accuracy
beyond the default HST archival pipeline, within a pixel scale of 0.03".
Within the HST imaging, two filters – F606W and F814W – are used in our
analyses due to their superior spatial resolution and depth when compared to
HST/WFC3 images. These bands also are bluer than the JWST data and thus
provide a blue base line for our SED fitting. It is clear that using these two
HST filters within CEERS is critical for measuring accurate redshifts and
other physical properties as this JWST dataset is missing the important F090W
band Adams et al. (2022).

####  2.3.2 JADES NIRCam Observations

The JADES field was observed with NIRCam (Rieke et al., 2023) which cover both
the GOODS-S and GOODS-N fields. The galaxies we use in this paper come from
the GOODS-S field data (PI: Eisenstein, N. Lützgendorf, ID:1180, 1210). The
observations of this field utilise nine filters: F090W, F115W, F150W, F200W,
F277W, F335M, F356W, F410M, and F444W, over an area of about 25 arcmin2.
Within these observations a minimum of six dither points were used with
exposure times ranging from 14-60 ks. We calculate that the $5\sigma$ depths
range from 3.4 to 5.9 nJy, within aperture sizes between 1.26 and 1.52 arcsec.
Across all filter bands, JADES ensures a high level of pixel diversity (Rieke
et al., 2023), thereby significantly reducing the impact of flat-field
inaccuracies, cosmic ray interference, and other issues at the pixel level. In
this paper, we utilize the publicly released JADES data and reductions.

####  2.3.3 SED Fitting

We use the JWST imaging data not only for the morphology and structure for the
Machine Learning applications, but also the SEDs constructed from the JWST+HST
bands. We fit these SEDs using the Bagpipes (Carnall et al., 2018; Carnall et
al., 2019) code to both the photometric and spectroscopic data for our sample
of systems. We do this for six parametric SFH models, including: log-normal,
delayed, constant, exponential, double delayed, and delayed burst—along with a
non-parametric Continuity model (Leja et al., 2019). These models are widely
accepted and have been used in various works (e.g. Carnall et al., 2023;
Endsley et al., 2023; Tacchella et al., 2023; Whitler et al., 2023; Looser et
al., 2023).

We carry out these fits by fixing the redshift to the spectroscopic redshift
in all cases throughout this paper. Within these fits, we use Log10 priors for
the dust properties we fit. We select Log10 priors as we expect high redshifts
galaxies to be young, with a lower metallicity. We set prior limits for
metallicity in the range of $[1\text{e-06},10.0]\,\text{Z}_{\odot}$, dust
prior in the range of $[0.0001,10.0]$ in $A_{\text{V}}$, ionization parameter
$\mathrm{Log}_{10}(\mathrm{U})$ in range of $[-4,-2]$, the star formation
start time is placed at 0.001 Gyr, the time assumed for star formation to stop
is at $t_{\text{U}}$ – the age of the Universe at the observation. We use a
Kroupa IMF as well as Bruzual & Charlot (2003) SPS models, and the Calzetti et
al. (1994) dust attenuation model is implemented. As we use dust attenuation
inferred from SED fitting, which is not significantly affected by different
SFHs, we have chosen to present results inferred from our fiducial model, the
log-normal SFH. The one limitation to using these SED fits is that we assume
the dust extinction law is Calzetti. We largely keep this as this is by far
the most common dust extinction line used to measure the photometrically
derived properties of galaxies and one goal of this paper is to determine how
accurate this assumption is based on an independent derivation.

###  2.4 Deep Learning CNN Model

####  2.4.1 Data Augmentation

Whilst we have many simulated galaxies from the Illustris TNG, the more
imaging used in the training the better in terms of performance for a CNN
model. We thus carry out an augmentation of modifying our existing origianl
sample to create a large one derived from this original imaging.

To increase the number of images for our use, the simulated TNG images were
augmented to increase the training set size. First, each image was rotated by
90, 180 and 270 degrees clockwise. The training dataset was then balanced to
have a more even distribution of predictive values. Augmentation of images
included : image rotation, image flip across the x or y-axis, addition of
Gaussian noise, or applying a histogram of gradients (HOG) to the image.
Without augmentation, outlier values are often ignored, as it is a small
subset of the data (Longadge & Dongre, 2013). We also want to use augmentation
to balance the distribution of the values in the dataset. As the dataset has a
Gaussian distribution, the machine is more likely to estimate values close to
the median of this dataset as this will have a small loss value, thus
appearing to be more accurate. Using a loss function such as mean squared
error (expanded upon in later sections) penalizes the machine more for wrong
guesses at the extreme, and so over the course of training the machine becomes
more conservative in its predictions. To account for this, we raise the
proportion of large values in the training set.

The augmentation of the smaller datasets helps supplement the amount of images
available for training and can hopefully lead the machine to be able to
predict and generalize to a wider range and variety of images. We want to use
good quality images to ensure better training results, so we impose a signal-
to-noise ratio (SNR) cut-off of SNR $\geq$ 5 on the images of galaxies to get
a set of clean data. Imposing this SNR cut-off cuts down the original images
we have to use from 33,376 to 6,620. Augmentation helps increase the amount of
usable images to 25,208. The set of images is split into two groups, 85$\%$ in
the training set and 15$\%$ in the testing set, where the training set is
defined as the dataset used to train the machines. During training, a smaller
subset of the training set of data is further split from the main training
data. After each epoch of training, the CNN model will test the machine
against this smaller subset of data, known as the validation set (Wang et al.,
2016). A validation set is used as a proxy for the testing set inside the
training period. As the model has not seen the validation set of images in the
training epoch, it can be used to estimate whether or not the machine should
be early-stopped. On the other hand, the testing set is used after training to
assess how well the machine performs as it is a set of images that the machine
has not seen at all during training.

####  2.4.2 CNN Model Set-up

The Convolutional Neutral Network (CNN) model built for this analysis uses the
tensorflow and keras package. To optimize the tuning algorithm, we used the
keras-tuner package. The CNN model consists of two main sections, the
convolution layers and the neural network layers. A convolutional neural
network is named after the convolution layers, which use a number of different
matrices to select features of the images, such as borders of objects. This
layer uses the convolution operation to convolve two sets of data, here being
the input and the filter, to create a feature map. This feeds into the fully-
connected layers which works on sorting inputs or calculating properties (For
more details on CNNs see Albawi et al. (2017)).

There are two main variables in a convolution block, the number of filters in
each layer and the number of layers. We use a fixed kernel size of 3 by 3
units for the convolution layers, followed by a BatchNormalization layer and a
2 by 2 MaxPooling layer. The kernel, or filter, mentioned is used to convolve
the input data. Filter weights are finetuned in the training process so the
convolution process shows features from our images. The Pooling layer is
another process to help particular features stand out by aggregating pixels
together to maximise features. Previous work from Cheng et al. (2020) used
AveragePooling, but here we find that the loss is smaller when MaxPooling was
used. The BatchNormalization layer works to normalize the input distribution
during training to prevent large internal shifts, known as internal covariate
shift (Ioffe & Szegedy, 2015). An activation function is applied as a non-
linear operation after the CNN layers and we use the rectified Linear Unit
(reLU), which follows the formula $f(x)=max(0,x)$, a common activation
function that has shown to perform well for CNNs (Agarap, 2018).

The data is then flattened into a 1D array before being passed into the neural
network layers, referred to as Dense layers below. Neural networks consist of
different number of layers that assign weights to features found by the
convolutional layers in order to predict an expected value. The number of
filters in the layers determines the complexity of the model. Right before the
output layer, we employ a dropout layer which shuts off a percentage of the
output nodes (50$\%$ here). This is done to prevent outputs from coming from
only a small subset of nodes and spreads the learning amongst all nodes, a
common approach to prevent overfitting (Srivastava et al., 2014). This dropout
layer is used in training only, so all output nodes are used during evaluation
of testing data, which should help performance when the model predicts using
testing data.

We utilise hyperparameter training to help determine the optimal value for
each variable in our model. The complexity of neural network machines mean
that there are a large number of variables and an even larger variable space
to explore. Each convolution and dense layer includes variables such as the
number of filters, activation function, batch size, and even kernel size.
Within the structure of the machine there are even more variables such as the
choice of learning rate, learning algorithm, loss values, and activation
functions. In hyperparameter training, variables are given a range and step,
which will be fine-tuned over the hyperparameter training process to give the
smallest loss value (Yu & Zhu, 2020). For example, the number of filters in a
convolution layer was set within a range between 4 and 64. The hyperparameter
tuning runs through different combinations of parameters to try to pinpoint an
optimal set of parameters that could perform the best on the testing data.

Other hyperparameters included the learning rate of the optimizer function
Adam, the Adaptive Movement Estimation algorithm (Introduced in Kingma & Ba
(2014)). Values were allowed to vary between 0.01, 0.005, 0.001, 5 $\times
10^{-4}$ and 1 $\times 10^{-4}$, but centered on 0.001 as recommended as per
Kingma & Ba (2014). The learning rate helps determine how much the machine
tunes its weights in response to results of each trial. Large learning rates
can cause more variability, leading to longer training times and reach sub-
optimal results. However, small learning rates requires a longer time for the
machine to move through the variable space (Wilson et al., 2017). In tuning,
the different learning rates are tested and the learning rate which results in
lower evaluation loss values is used. The tuned hyperparameters we use are
listed in Table 1. Performance is assessed by the loss function. Here we use
the percentage error function. Other common loss functions, such as mean
squared error, yield small error values due to the small values and cause poor
training results. Keras-tuner offers multiple optimization methods, where we
chose to use the Bayesian Optimization algorithm. The other optimization
methods, such as grid-search or random-forest walk, took a longer time to
traverse the variable space in comparison.

Figure 5: Machine Structure: Machine structure for the one band input for the machine predicting E(B-V) values. The numbers written on top of the CNN layer gives the dimensions of the particular layer. For example, 36@32x32 indicates 36 layers of dimensions 32 by 32. For the Dense layers on the right hand side, 1x64 means the layer has 64 nodes. Parameter | Range | No. of layers
---|---|---
CNN filters | 4 - 64 | 1 - 4
Dense neurons | 8 - 64 | 1 - 4
Learning Rate | 0.01 - 0.0001 | -
Batch Size | 16 - 64 | -
Table 1: Hyperparameters: The range of parameters used in hyperparameter
training, tuned to optimize accuracy. All CNN and Dense layers in a machine
structure are given the same range. During hyperparameter tuning, the
optimization algorithm tests different sets of parameters to find the set that
returns the lowest loss value.

Observations at different wavelengths can show different properties. We use
three bandpass images (F277W, F356W, F444W) to utilise these distinct
morphological features. In a three-input model, each image is taken into an
individual convolutional block and then condensing the three inputs into one
array for the dense layers. We expect better predictions as the wavelength
dependency of dust extinction should show up and be compared across different
bandpass images. A drawback is that optimizing for multiple inputs increases
the number of parameters to tune and requires more time and memory needed
during training. We set 200 trials for the hyperparameter tuning process,
where each trial tested a different set of parameters on the machine. Training
is cut short if the validation loss did not improve over 5 epochs of training.
This helps cut down on the time needed as poorly performing models are
terminated early. We chose the machine structure of three CNN layers and four
dense layers which resulted in the lowest loss values for $E(B-V)$,
illustrated in Figure 5. Due to time constraints, we used the same
configuration for models for the other properties.

Figure 6: Machine learning E(B-V) Predictions : (Top) Comparison of the simulated ’true’ $E(B-V)$ values against the machine predicted results with one band input on the top, and the three band inputs on the bottom. The red line charts where the predicted value is equal to the true value, and deviation from this line shows a bias in the distribution. We show the distribution of the predicted value in blue bars and the true value in a red outline in the histogram. On the right hand side, the histogram of the difference between the true and predicted values, calculated by subtracting the predicted from the true value. A longer trailing tail towards the right of the distribution show a bias of the machine towards under predicting values, which can also be seen in the difference in overall distribution on the small histogram and scatterplot on the left. (Bottom) The scatterplot is more concentrated with less scatter when compared to that of the one input, but still shows under-prediction at larger values when the scatter deviates away from the red line. This also manifests in the histogram of differences on the right, which is skewed slightly right of the red $x=0$ line. Compared to the one input histogram on top, the differences from the three input are generally smaller, indicating a better fit. Figure 7: Machine learning $\textup{A}_{V}$ Results : (Top) Comparison of the machine predicted $A_{V}$ results against the simulation based ’true’ values of dust extinction $A_{V}$, with the two plots at the top showing results from the one band model. On the left scatter plot, predictions cluster around the red (true = predicted) line but our ML model underestimates some values at the extremes. The distribution of true values is skewed more towards the left than the distribution of the predicted values. This is reflected in the distribution of their differences on the right, where the histogram has a very slight tail towards the left, showing that the predicted values tended to be larger on average than the expected true value. Therefore our ML method is slightly over predicting the correct $A_{V}$ values for galaxies based on its training. (Bottom) Predictions from the three band model. The left scatterplot shows a tighter distribution around the red line as compared to the one band model. A smaller histogram comparing the distribution of predicted and true values show similarly shaped distributions. On the right, the histogram of the differences shows that the errors are slightly better than the one input model on the top. However, there is also a tail towards the left, showing a similar tendency of over-prediction of dust extinction as the one input model. As can be seen the three band model has a tighter distribution of differences from true minus prediction, but the distribution is more skewed.  Figure 8: sSFR Results : (Top) Comparison of the machine predicted results against the true values of sSFR in the units of log (yr-1). The distribution of predicted values for the one input has a limited range and is concentrated towards the median. There is clearly a sharp line at the largest value that the model can predict, seen in the scatterplot and histogram of predicted values. On the right, there are a number of outliers, but the overall distribution of the differences between true and predicted values is more symmetrical. (Bottom)  The scatter strength for the three input model for sSFR is clearly weaker, and the distribution shows that the model predictions have a smaller range than the one input model and the model over-predicts at the median values. There is also a similar line where the machine is not able to predict any larger values. The difference between true and predicted values is similarly symmetrical. However, the average difference is larger than that of the one band input. Evaluation of Predicted Values |
---|---
| E(B-V) | AV | RV | sSFR
| 1 Band | 3 Band | 1 Band | 3 Band | 1 Band | 3 Band | 1 Band | 3 Band
MAE | 1.36 $\times 10^{-2}$ | 1.31 $\times 10^{-2}$ | 8.91 $\times 10^{-2}$ | 6.85 $\times 10^{-2}$ | 3.4817 | 2.8892 | 4.56 $\times 10^{-2}$ | 6.88 $\times 10^{-2}$
MSE | 3.55 $\times 10^{-4}$ | 2.53 $\times 10^{-4}$ | 1.52 $\times 10^{-2}$ | 9.94 $\times 10^{-3}$ | 45.9 | 18.7 | 4.60 $\times 10^{-3}$ | 8.16 $\times 10^{-3}$
Standard Deviation $\sigma$ | 1.72 $\times 10^{-2}$ | 1.08 $\times 10^{-2}$ | 0.121 | 9.94 $\times 10^{-2}$ | 6.2325 | 3.4815 | 6.71 $\times 10^{-2}$ | 8.95 $\times 10^{-2}$
Variance $S^{2}$ | 2.95 $\times 10^{4}$ | 1.17 $\times 10^{-4}$ | 1.47 $\times 10^{-2}$ | 9.89 $\times 10^{-3}$ | 38.8441 | 12.1205 | 4.50 $\times 10^{-3}$ | 8.01 $\times 10^{-3}$
Table 2: Comparison of Predicted Values :  To compare and evaluate the
difference between the 1 input and 3 input machines, we look at how well the
machine performed overall, illustrated in the differences between the true and
predicted values. We compute the mean average error, mean squared error,
standard deviation, and variance of the distribution of the differences to
compare how well the one-input machine performs to the three-input for each
different value. Overall, the three-input model seems to perform slightly
better than the one-input model.

##  3 Results

###  3.1 Training

We train and test our CNN models on three different quantities of interest
($E(B-V)$, $A_{V}$, sSFR) using one (F277W) and three (F277W, F356W, F444W)
images as input, for a total of six different tests run. A set of values of
$R_{V}$ is calculated using the relationship from Equation 1. Our aim is to
determine how well the visual image and the morphological features of a galaxy
can be used to calculate its dust properties. By using a single image and
three images, we can also investigate the potential of a CNN model in
evaluating morphological features between different wavelengths for measuring
the dust content.

The result from training the machine with one input (F277W) is shown in Figure
6. We compare the true and predicted values on the left, plotting the values
against each other in a scatterplot and comparing the distribution in the
histogram on the right. The shape of the distribution indicates that the
trained machine tends to under-predict actual values, and the scatterplot of
values show a good linear correlation between both values upon the identity
function ($x=y$) represented in a red line. A set of good predictions should
follow this red line, whereas our one input machine results show a wide
clustering around this red line and a couple of outliers. Overlaying the
scatterplot is a 2D probability density plot drawn to include [10, 30, 50, 70,
95] percent of the total values which helps illustrate how clustered these
predictions are.

For the one input $E(B-V)$ model, the scatterplot and probability density
contours show a slighlty wide spread. The density contours show that the
majority of the points lay towards the left of the red line, showing that our
model generally under-predicts values. This is shown in the small histogram in
the same plot, where the peak of the blue histogram (Predicted Value) is to
the left of the brown histogram (True Value). To evaluate how well our machine
can predict colour excess, we look at the difference between the true and
predicted value on the histogram on the right. This distribution goes to zero
if the predicted and true values are the same, represented by the red line.

To quantify these differences better we calculate the mean absolute error
(MAE) to illustrate how different the predictions and the expected value are
using

$MAE=\frac{1}{N}\sum^{N}_{i=1}|y_{i}-\hat{y}_{i}|$ (3)

The value of MAE is unable to differentiate if the model under-predicts or
over-predicts by itself as it has no direction. Here, the distribution of the
differences skews left, showing a non-zero (0.0136) MAE for the differences
and indicating that the machine tends to under predict the colour excess.
Overall, the distribution is relatively symmetric aside from the tail skewing
left. Predictions from the three input machine shows similar values, such as a
wider clustering and under-prediction. From Table 2 the average differences
for the 3 Band predictions of colour excess is $=0.013$, which is very close
to the results from the single band trained machine. Conversely, the
distribution from the three Band predictions have a smaller standard deviation
and variance, ($\sigma=$ 0.0172 to 0.0108). We observe similar trends in other
values of the dust extinction and sSFR.

Figure 7 compares the results of dust extinction values ($A(V)$) using one
input and three input. The predictions of $A_{V}$ show tighter clustering as
compared to values of $E(B-V)$ from the scatter plot and density contours with
less numbers of outliers. The histogram shows a slight right-leaning bias,
indicating that there is also an over-prediction. This is also evident in
looking at the histogram of the differences between the true and predicted
values which has a trailing tail to the right. Results from using three bands
to predict dust extinction shows tighter clustering and more accurate
predictions as compared to the one band results. The distribution of the
differences of one and three input predicted values has a smaller average (MAE
= 0.09 to 0.07) and a smaller standard deviation (MAE = 0.012 to 0.099)
compared to the differences using one input. Overall, the range of differences
is slightly larger for the one input than the three input.

With both values of $E(B-V)$ and $A_{V}$, we can calculate the R-value using
Eq. 1. As the $R_{V}$ value is calculated using two predicted values, we
expect larger errors. This is reflected in the larger spread of $R_{V}$
values. The shape of the distribution shows an over-prediction, also seen in
the histogram of differences, skewing left. This may be due to the general
trend of smaller than predicted $E(B-V)$ values causing large $R$-values.
While the three input model is comparatively better, the same trend is
observed. Differences between the true and simulated $R_{V}$ values from the
three input model are overall smaller than that of the one input, as well as a
smaller average (MAE = 3.48 and 2.89) and standard deviation ($\sigma=$ 6.23
to 3.48), possibly due to the one input models for both $E(B-V)$ and $R_{V}$
have larger errors on average compared to the three input models.

The final value we test and measure is the specific star formation rate
(sSFR), represented in log10 yr-1 units. Figure 8 shows the results of the
machine training. One thing to immediately take away form this is that the ML
predictions for the sSFR are not as good as for the dust extinction values.
Star formation remains a challenging feature to measure with machine learning
methods as also found in other papers such as Euclid Collaboration et al.
(2023). Another odd feature of the predictions is the inability to predict
larger sSFR values as there is a sharp line on both one and three input models
in both the scatterplot and the histogram. While there are not many outliers
in the predictions from the scatterplot, the correlation is not as strong as
compared to those for dust extinction or colour excess. The distribution of
the differences between the true and predicted values is quite symmetric
without a tail in either direction. It is interesting to note that the sSFR is
the only property tested where the three input model did not perform better
than the one input. Both the average difference and standard deviation from
the one input are smaller than that of the three input, indicating that even
though the range of differences is larger from the one input, the distribution
is more concentrated. This type of regression analysis has been shown to work
well on imaging, but also using photometry, to measure other galaxy
properties, such as structural properties, redshift, stellar mass ,and star
formation rates (e.g., Tohill et al., 2020; Euclid Collaboration et al., 2023)

Figure 9: Predictions of the specific star formation rate (sSFR) values for
the JWST galaxy samples : (Left)  Scatterplot comparing the two sets of values
of sSFR generated using the 10 Myr and 100 Myr of star formation in the
Bagpipes code. For sSFR, there is a much larger difference between the two
sets of values. Since the simulated images used for training were generated
with Illustris using a 100 Myr time-scale, we compared our predictions to that
of the 100 Myr set of Bagpipes data. (Middle)  Predictions of sSFR values
using the one band model (Top) and three band model (Bottom). Both models can
only predict a limited range of sSFR values compared with the Bagpipes
results. It appears that predictions from the one input model are more
symmetrical and have a larger peak at the median, compared to the three input
model. (Right)  The differences between the predicted and Bagpipes values are
shown, with the difference with one input on top and three inputs on the
bottom. Both have a similar distribution which skews slightly right,
indicating over-prediction by the machine.

###  3.2 Application to JWST imaging

Figure 10: Predictions of $A_{V}$ values for the JWST galaxy samples : (Left)
Two sets of values for the physical properties of our JWST galaxy sample as
generated using the code Bagpipes, one assuming a 10 Myr star formation star
formation scale and one using a 100 Myr time range. This scatterplot shown
here compares the difference between these two sets of values against the
predictions by our machine learning method. For dust extinction, there does
not seem to be much difference between the two sets of Bagpipes values, and
neither show a strong correlation with our machine predictions. (Middle)  The
predictions of dust extinction values using the one band model (Top) and three
band model (Bottom) on our JWST sample. The blue bars of the predicted values
show the machine is predicting large values of $A_{V}$ compared to the SED
fitting method, especially at small values. To show the general trend of
predictions, a probability density curve (PDF) is overlaid on the histogram,
showing that both one and three band models are extremely similar. (Right)
The differences between the predicted and Bagpipes values for the dust
extinction, with the difference of one input band shown on top and three input
images on the bottom. Both show similar distributions, with a smaller MAE for
three input (0.26 vs. 0.24). While the standard deviation and variance for the
three input also indicate closer predictions to the Bagpipes values,
differences are slight compared to the one-band predictions. These differences
are on the same level as when comparing the Bagpipes to the Meurer method as
show in Fig 11. Figure 11: Comparison of the BagPipes and Meurer relation:
Plot showing the difference in the measurement of AV with the code BagPipes
and those calculated using the Meruer relation. The range of differences
between the values of BagPipes and the Meurer relation appears similar than
the range of values obtained using predictions with the CNN models and
BagPipes, shown in Fig 10.

The release of JWST imaging allows us to test our machine which has been
trained on simulated JWST data on real JWST data. To do this, galaxies with a
confirmed NIRSpec redshift at $\geq$ 6-7 were selected from Duan et al.
(2023). These are amongst the earliest galaxies which have confirmed
spectroscopic redshifts at the redshifts of interest. Figure 4 shows the
sample of these JWST images in the CEERS and JADES fields we use. Parameters
of dust extinction and sSFR were calculated using the Bagpipes code using the
full SEDs to compare against the predicted outputs by our machine.

Two sets of properties from Bagpipes are calculated using 10 and 100 Myr star
formation time-scales respectively. These time-scales affect the retrieved
sSFR values, as can be seen in Figure 9, a scatterplot showing the difference
of the two sets of parameters. In the 100 Myr set (red points) there are no
values of sSFR larger than -7.75, whereas the 10 Myr SFR set (blue points) has
a larger range of sSFR values, up to -7. Since the models were trained on
Illustris images generated with a star formation timescale of 100 Myr, we
compared our predictions to the set of data using a 100 Myr timescale.

Figure 10 shows the comparison of dust extinction values when using one band
and three band input machine predictions and values from Bagpipes in the JADES
field. On the very left, we compare the set of Bagpipes data at the 10 and 100
Myr timescales. While the values from using a 100 Myr timescale are, in
general, slightly larger than those from a 10 Myr timescale, the differences
appear minimal. In the middle, we show the predicted values compared to the
Bagpipes values, with the one band predictions on top and the three band
predictions on the bottom. Our predictions are shown in the blue histogram
while Bagpipes values are shown in a brown outlined histogram. Between the two
different models, the three input appears to be able to predict a wider range
of values, but both models have a tendency to predict larger dust values than
Bagpipes.

On the right, we take the difference of the Bagpipes and predicted values, as
this helps us visualise how close the individual predictions are. The shape of
the distribution of both are similar, with a slight skew towards the left,
indicating an over-prediction in values compared to the SED fitting. Overall,
the MAE from the one input is $=0.26$, a touch larger than that of the three
input $=0.24$. The standard deviation and variance from the one input is also
slightly larger. This continues a similar trend that also appears in test
results, where the predictions from the models skew larger and the model using
three inputs is slightly better than the one input.

We also compare different methods for finding AV in Figure 11 using Bagpipes
and the Meurer relation (Meurer et al., 1999). This relationship between dust
extinction and the UV-continuum slope $\beta$ is as follows :

$A_{IRX-\beta}=4.43+1.99\beta$ (4)

At z $\sim$ 0, this relationship has been shown to be a good predictor of dust
extinction in galaxies, but does not always generalise to high-redshift
galaxies (Koprowski et al., 2020; Liang et al., 2021).

This is a common way to determine the value of $A_{V}$ based on the UV slope,
and it is a method which is independent of the SED fitting discussed earlier.
The way we carry the measurement of $\beta$ out is explained in detail in Duan
et al. (2023), whereby we measure the $\beta$ slope for our galaxies through
direct measurements of the slope of each NIRSpec spectrum within the UV range
by fitting a power-law and measuring its slope. As we are using the actual
spectrum for this measurement, we are directly measuring this slope and not
inferring it from photometry. The comparison of this ’Meurer’ method with the
Bagpipes measurements is shown in Figure 11.

This comparison between the Bagpipes and Meurer values also shows large
differences and a larger standard deviation as compared to that of our CNN
machine predictions, $\sigma$ = 1.52 to 0.34 (Figure 10). The range in the
differences is also smaller from our machine predictions, meaning that the SED
fitting method and our machine learning method agree better than the Meurer
relation and SED fitting. This shows that our machine is at least comparable
in accuracy with those based on the Meurer relation, which is commonly used to
find the value of $A_{V}$.

However, what we find using all three of these analysis methods is that the
dust content of distant galaxies observed with JWST is relatively low with
values $A_{V}<0.6$ and on average around $A_{V}\sim 0.3$. This means that
distant galaxies, those with higher star formation rates especially, which are
the ones that have successful spectroscopy, are low in dust content. This is
opposed to lower redshifts where dusty galaxies can have a large impact on the
galaxy population.

As mentioned earlier in this section, the other value that we compared is
sSFR. Figure 9 illustrates the results we obtained for sSFR using our models
on the JWST samples. Again, the leftmost scatterplot shows the difference
between using 10 and 100 Myr timescale, where the sSFR values from the 100 Myr
are smaller. This scatterplot shows the predicted sSFR values on the x-axis
and on the y-axis the Bagpipes values. On this plot are shown the range of
values of the 100 Myr star formation scale as red points, which are much
smaller than the blue points showing the 10 Myr scale. The values of sSFR
predicted by our model correlates closer to that of the 100 Myr timescale
Bagpipes, which indicates that the machine is predicting reasonable sSFR
values. In the middle panel we compare the values of the 100 Myr timescale
Bagpipes sSFR and predicted sSFR, with predictions from the one input model
shown on the top and three input model on the bottom. Both models are not very
accurate and are not able to predict the full range of the sSFR values from
Bagpipes. Furthermore, the shape of the predictions shows a sharp peak which
is quite different to that of the Bagpipes values. On the rightmost panel we
examine the differences between the sSFR values from our models and Bagpipes.
There is a large range and the distribution is skewed towards the right, where
the model’s over-predict the values. For sSFR, the results of the one input
model is similar to that of the three input model, with a similar MAE (0.18 to
0.19) and standard deviation (0.20 to 0.21). This reflects the testing results
on simulated data, in which the three input model performs slightly worse but
neither are able to predict extreme sSFR values on both ends.

##  4 Discussion

We discuss our results both in terms of the use of machine learning for
measuring dust properties of distant galaxies, as well as the results that we
find when we apply the models to JWST imaging data. Both of these issues are
very important in extragalactic astronomy, as dust is a key component of
galaxies and the formation of stars and is a significant aspect in the
observability of galaxies at different wavelengths. In addition, dust
evolution in galaxies is still a major mystery and finding new ways to measure
it is important for a full consensus of galaxy evolution.

We have shown that based on stimulated imaging data that we can retrieve with
a high accuracy the dust content of galaxies as measured through the $A_{V}$
values. Results from our testing show that using only one input (F277W) and
using three inputs (F277W, F356W, F444W) yield similar results for estimating
all of the properties we examine. This was slightly unexpected, as it might
seem that the ’colour’ information provided by the multi-bands would give some
indication of the properties of dust and star formation. Properties such as
colour differences and dust extinction occur because dust absorbs shorter
wavelengths more efficiently, so these properties are best extracted with
inputs of different wavelengths. SFR has also been strongly correlated with
SED shape, although we see little difference here between the one band and the
three band imaging when inputted into our machine.

However, one of the strengths of CNNs is its ability of feature extraction in
images, which we utilize by looking at the morphology of galaxies. Thus a
major conclusion is that even in a single band it is possible to understand
aspects of the dust content of galaxies, as well as of star formation. This
has already been shown in the case of SFR for measurements using single bands
(e.g., Euclid Collaboration et al., 2023). As we focus in this paper on the
difference in morphology between the different bands in the 3-band input, the
similar predictions indicate that the morphological differences at different
wavelengths do not provide substantial improvements in helping the model
predict dust and sSFR values. We find that the three input model performs
marginally better overall, but the small dataset for the JWST data used here
makes it difficult to assess the accuracy and generalise between the one and
three input models on actual data.

A difficulty we face in taking models trained from the simulated data and then
applied to the observational data from JWST is what is called dataset shift.
Dataset shift occurs when the training and testing distribution are
fundamentally different (Moreno-Torres et al., 2012). This can make it
difficult for the model to generalize its learning from training data and
applying the model to testing data, yielding poor results. Here we find a
notable possible dataset shift between the training data and the set of
Bagpipes values that we use. The data simulated from Illustris uses an
instantaneous star formation timescale of 100 Myr (Pillepich et al., 2017). On
the other hand, we had two sets of testing data from the JWST images,
calculated from Bagpipes, using a star formation timescale of 10 and 100 Myr,
as well as using the Meurer relation. We find first that through any method
the dust content of galaxies at $z\sim 6-7$ are relatively low, within the
lower regime of our training set, and that there is within these values
considerable scatter is present.

The leftmost plot in Figure 9 shows how the two sets of Bagpipes values
correlate with our predictions, trained on a timescale of 100 Myr. The range
of sSFR values between those predicted by our model is also close to the range
predicted by the 100 Myr SFR-timescale values from Bagpipes, showing how
important the training data is in getting accurate predictions. The
predictions our models made on the JWST data also reflects the range of sSFR
values of the simulated galaxies. Extreme values from Bagpipes that were not
represented during training makes it more difficult for the neural network to
predict. This is one reason why sSFR is difficult to measure in machine
learning as the values of real galaxies have longer tails in this value’s
distribution at low and high values than other properties such as the dust
extinction.

The effects of the 10 Myr and 100 Myr SFR-timescale dataset shift is not as
obvious with dust extinction, shown in the leftmost scatterplot of Figure 10.
There is a small difference in the values of AV from Bagpipes using 10 and 100
Myr SFR-timescale. However, the range of values used in training from
Illustris for dust extinction was much larger, up to A${}_{V}>$ 2\. When we
tested the models with JWST data, the models were able to retrieve small
values of dust extinction.

The uncertainty of dust measurements at the high-redshift regime also makes it
difficult to determine how accurate our model is. Our predictions estimate
that there is some amount of dust attenuation on these early JWST galaxies,
but not as high as at lower redshifts. The simulated data that we trained the
CNN models on had a wide range of dust extinction values ($A_{V}>2$), but
groups of high-redshift galaxies observed by JWST have been shown to be
extremely blue (Adams et al., 2022; Atek et al., 2022; Castellano et al.,
2022; Finkelstein et al., 2022; Naidu et al., 2022; Ferrara et al., 2023) with
very low amounts of dust attenuation (down to $A_{V}$ < 0.02) (Furtak et al.,
2022). This signifies a significant difference between the properties of these
high redshift JWST galaxies and the galaxy samples we trained the CNN models
with. It is a sign that dust has not had time to build up within galaxies at
the time that we are observing them at $z\sim 6-7$.

The results presented here utilise a CNN machine learning tools with a
structure of three convolution and four dense layers. However, other popular
CNN models (i.e. LeNet, AlexNet, VGG-16) utilise far more convolution layers
and larger number of variables, such as the kernel size or number of filters.
During the tuning process, our models converged to the maximum number of
filters we set. This may indicate that more filters could help better capture
the features of the galaxies. However, more hyperparameters would lead to a
significant increase in parameter space, as each successive layer builds upon
the number of outputs of the previous layer. With longer training time and
increased computing power, the structure could be further tuned for a better
performing model.

Future work in this direction could include incorporating MIRI images into the
training dataset when available. This will not work for all galaxies as MIRI
detections of such high redshift galaxies will be difficult except when
examining very long exposure times (e.g., Li et al., 2023). The longer
wavelength capabilities of deep MIRI data might be able to observe even higher
redshift galaxies as thus find and locate spectral properties inaccessible in
the NIR wavelengths. Studies such as Vika et al. (2015); Mager et al. (2018)
have shown that morphology has a strong wavelength dependence, so MIRI images
may be able to contribute more features to improve the prediction accuracy of
the machine learning method. Ultimately, if we can find a direct approach to
dust extinction we can train samples on large collections of galaxies with
these measurements which may be a superior method than using simulated
imaging.

##  5 Summary

We present in this paper a Machine Learning analysis of simulated galaxy
images from Illustris TNG to retrieve the physical properties of dust
extinction and specific star formation rate in high-redshift galaxies, purely
from JWST imaging. Our results show that the CNN model we construct and
calibrate can reproduce these values well within the simulated images.

For this analysis we use simulated images from Illustris created as imaged in
the JWST bands and within NIRCam imaging specification, including the commonly
observed F277W, F356W and F444W filters. We create a set of models using only
the F277W band as an input, and another model using all three of these
bandpass images as inputs. We find that the three input model perform slighlty
better across $E(B-V)$ and $A_{V}$, but performs slightly worse at predicting
sSFR. We use MAE and MSE values to judge how close the predictions are to the
real values - for the colour excess E(B-V), the MAE value of the one input
model is 1.36 $\times$ 10-2 which is only slightly larger than that of the
three input, giving a MAE of 1.31 $\times$ 10-2. The same trend whereby the
MAE is slightly smaller than MSE for the three input model is seen in the
retrieved dust extinction AV and R-values. Using standard deviations and
means, we find again that the three band model appears to be more robust and
performs slightly better against the one input model in estimating colour
excess, dust extinction and R-value.

We compare our machine learning results to fits from SED fitting models using
BagPipes where the input is the entire JWST multi-wavelength data to determine
how consistent these approaches are. The one input model predictions of sSFR
agrees slightly better with the BagPipes values compared to the predictions of
the three input model. The MAE of the one input model is 4.56 $\times$ 10-2
compared to the MAE of the three input model, 6.88 $\times$ 10-2. The standard
deviation of one input is also smaller than the three input, with a value of
6.71 $\times$ 10-2. As effects of colour excess and dust extinction are
calculated from the differences between different bandwidths of images, it is
reasonable that the three input model is more robust and performs better than
the one input model. However, we observe similar values and the error from
both machine learning runs.

Data taken from JWST allows us to test our machine learning methods on
observed galaxy images. Using a sample of high redshift galaxies from the
JADES and CEERS data release previously analysed in Duan et al. (2023) which
have spectroscopic redshifts, we compare our predictions against values
estimated by SED fitting methods from Bagpipes. Thus, we are able in this
paper to compare dust measures from both the traditional SED fitting technique
and those based on our new formalism. In general, we find similar trends as
from training when comparing between these two. For dust extinction, the MAE
of one input predictions is 0.26, slightly larger than the MAE of three input
predictions, which is $\sim 0.24$. In values of sSFR, the one input has a
slightly smaller MAE, 0.18 against 0.19, the MAE of the three input model.
However, we do not know which of the measurements, either the SED fitting or
the ML derived values, are ’correct’. We do find that both methods give low
dust extinction values for distant galaxies, thus suggesting that dust has not
built up to a significant amount in the earliest galaxies (see also Austin et
al. 2024, in prep).

We demonstrate this general problem of measuring measure of dust content from
e.g., AV values by comparing the results using the $\beta$ method from the
Meurer relation. Compared to the values from the Meurer relationship, our ML
predictions have a similar average error, but a smaller standard deviation
(SDMeurer = 0.89 against SDCNN = 0.36). The errors show that our new machine
learning method is comparable to other, more traditional, methods used to
determine dust attenuation.

In conclusion, we find that the CNN model is able to predict dust values well,
with a smaller than expected difference between the performance using one and
three bandwidth images. Applying the models to JWST galaxies showed some
potential limitations with the predictions of CNN models compared to SED
fitting. However, what is clear is that this method can be applied in bulk
successfully to derive a measure, within some uncertainty, compared with full
SED fitting methods.

## Acknowledgements

We acknowledge support from the ERC Advanced Investigator Grant EPOCHS
(788113), as well as studentships from STFC. LF acknowledges financial support
from Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brazil
(CAPES) in the form of a PhD studentship. This work is based on observations
made with the NASA/ESA Hubble Space Telescope (HST) and NASA/ESA/CSA James
Webb Space Telescope (JWST) obtained from the Mikulski Archive for Space
Telescopes (MAST) at the Space Telescope Science Institute (STScI), which is
operated by the Association of Universities for Research in Astronomy, Inc.,
under NASA contract NAS 5-03127 for JWST, and NAS 5–26555 for HST.

## Data Availability

The inclusion of a Data Availability Statement is a requirement for articles
published in MNRAS. Data Availability Statements provide a standardised format
for readers to understand the availability of data underlying the research
results described in the article. The statement may refer to original data
generated in the course of the study or to third-party data analysed in the
article. The statement should describe and provide means of access, where
possible, by linking to the data or providing the required accession numbers
for the relevant databases or DOIs.

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