# Construction of a far ultraviolet all sky map from an incomplete survey:
Application of a deep learning algorithm

Young-Soo Jo1, Yeon-Ju Choi2, Min-Gi Kim3, Chang-Ho Woo3, Kyoung-Wook Min3,
and Kwang-Il Seon1,4
1Korea Astronomy and Space Science Institute, 776 Daedeok-daero, Yuseong-gu,
Daejeon 34055, Republic of Korea
2Korea Aerospace Research Institute, 169-84, Gwahak-ro,Yuseong-Gu, Daejeon,
34133, Republic of Korea
3Department of Physics, Korea Advanced Institute of Science and Technology,
291 Daehak-ro, Yuseong-gu, Daejeon 34141, Republic of Korea
4Astronomy and Space Science Major, University of Science and Technology
(UST), Korea, 217 Gajeong-ro, Yuseong-gu, Daejeon, 34113, Republic of Korea
E-mail<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

We constructed a far ultraviolet (FUV) all sky map based on observations from
the Far Ultraviolet Imaging Spectrograph (FIMS) aboard the Korean
microsatellite STSAT-1. For the $\sim$20$\%$ of the sky not covered by FIMS
observations, predictions from a deep artificial neural network were used.
Seven datasets were chosen for input parameters, including five all sky maps
of H$\alpha$, E(B-V), N(HI), and two X-ray bands, with Galactic longitudes and
latitudes. 70$\%$ of the pixels of the observed FIMS dataset were randomly
selected for training as target parameters and the remaining 30$\%$ were used
for validation. A simple four-layer neural network architecture, which
consisted of three convolution layers and a dense layer at the end, was
adopted, with an individual activation function for each convolution layer;
each convolution layer was followed by a dropout layer. The predicted FUV
intensities exhibited good agreement with Galaxy Evolution Explorer (GALEX)
observations made in a similar FUV wavelength band for high Galactic
latitudes. As a sample application of the constructed map, a dust scattering
simulation was conducted with model optical parameters and a Galactic dust
model for a region that included observed and predicted pixels. Overall, FUV
intensities in the observed and predicted regions were reproduced well.

###### keywords:

radiative transfer – scattering – techniques: image processing – surveys –
ISM: general – ultraviolet: ISM

††pubyear: 2020††pagerange: Construction of a far ultraviolet all sky map from
an incomplete survey: Application of a deep learning algorithm–12

##  1 Introduction

Observations of the interstellar medium (ISM) in the far ultraviolet (FUV)
wavelengths (900–1750Å) are extremely useful as they provide important
information on the physical and chemical processes that occur among the
constituents of our galaxy. For example, emission lines of highly ionized
atoms provide clues on how Galactic hot gas is generated and cooled due to
interaction with the ambient environment (Jo et al., 2019). The FUV band also
contains many molecular hydrogen fluorescence lines, which are good tracers of
star-forming regions in molecular clouds (Jo et al., 2017). Furthermore,
because the diffuse continuum background is believed to be the starlight
scattered by interstellar dust, its observation helps us understand scattering
properties of the dust grains and geometries of molecular clouds, particularly
when using scattering simulations of stellar photons (Jo et al., 2012; Lim,
Min & Seon, 2013; Choi et al., 2013; Chollet et al., 2015). FUV continuum
intensity has also exhibited good correlation with H$\alpha$ intensity,
indicating that the two emissions may have common origins and similar
radiative transfer mechanisms (Seon et al., 2011a, b).

Despite its importance, there have not been many FUV observations in part due
to significant extinction effects at FUV wavelengths. There have been only two
notable FUV survey missions since the one in 1972 by the TD1 satellite
(Boksenberg et al., 1973). GALEX, launched on 2003 April 28, observed the sky
in two wavelength bands using a dichroic mirror: FUV (1350–1750 Å) and near-
ultraviolet (NUV: 1750–2850 Å). Its spatial resolution was 5-7$\arcsec$ in the
sky over a 1°.25 field (Martin et al., 2003; Morrissey et al., 2007). The
GALEX survey data have been used extensively, especially in regard to the
diffuse UV background (Murthy, Henry & Sujatha, 2010; Murthy, 2014a, b, 2016;
Henry, 2012; Henry et al., 2015; Jyothy et al., 2015; Narayan, Murthy &
Karuppath, 2017; Akshaya et al., 2018, 2019). Though not used frequently, low-
resolution spectroscopic data are also available from observations made with
an objective grism. Another FUV mission used a Far-ultraviolet IMaging
Spectrograph (FIMS), also known as Spectroscopy of Plasma Evolution from
Astrophysical Radiation (SPEAR), onboard the spacecraft Science and Technology
SATellite-1 (STSAT-1) launched on 2003 September 27 (Edelstein et al., 2006a,
b). FIMS was a dual-band imaging spectrograph with a short- (S-band: 900–1150
Å with 1.5 Å resolution, 4°$\times$5$\arcmin$ field of view) and long-
wavelength band (L-band: 1335–1750 Å with 2.5 Å resolution,
8°$\times$5$\arcmin$ field of view).Both bands have an imaging resolution of
5′. GALEX and the FIMS L-band possessed nearly identical spectral bands.
Nevertheless, both GALEX and FIMS did not cover the whole sky; GALEX
intentionally avoided the observation of bright regions to protect the
detector whereas the electrical power problems with STSAT-1 caused frequent
interruption and the early termination of FIMS.

A deep artificial neural network (DNN) is a subset of machine learning (ML),
composed of multiple interconnected layers of “artificial neurons” with
powerful optimization algorithms (LeCun, Bengio & Hinton, 2015). DNN, based on
automatic learning from massive data during the training stage, can capture
complex non-linear relationships in data by constructing hierarchical internal
representations. DNN is especially successful in image processing;
specifically, the convolutional neural network (CNN) adopts a feed-forward
neural network inspired by studies of visual recognition mechanisms in mammals
(Rawat & Wang, 2017). CNN generally utilizes a multi-layer architecture
consisting of multiple feature-extraction steps such as convolution, pooling,
and nonlinear activation layers. While CNN, which utilizes only current
inputs, is primarily suitable for image processing, sequential datasets (in
which the next step depends on the previous input data) can be modeled by a
recurrent neural network (RNN). The RNN algorithm includes a hidden state
memory that summarizes the previous input information. RNN has proven to be
particularly successful in natural language processing (Lipton, Berkowitz &
Elkan, 2015).

ML has become increasingly popular in astronomy studies, where enormous multi-
spectral datasets are produced from ground and space observations, and very
sophisticated analysis tools are required to extract meaningful information
(Ball & Brunner, 2010). For example, CNN was applied to studies of star-galaxy
distinction (Kim & Brunner, 2017), gravitational lensing (Schaefer et al.,
2018; Davies, Serjeant & Bromley, 2019), and photometric redshifts (Pasquet et
al., 2019). Naul et al. (2018) presented an unsupervised auto encoding RNN
that could reconstruct noisy, irregularly sampled astronomical data. An ML
technique called Support Vector Machine (SVM) used an optimal hyperplane in an
N-dimensional space to separate classes (Kovács & Szapudi, 2015; Pashchenko,
Sokolovsky & Gavras, 2018). Baron (2019) developed an outlier detection
algorithm based on unsupervised learning that could identify unexpected new
objects in image, spectral, and time-series datasets. Das & Sanders (2019)
estimated the age, distance, and mass of red giant stars using Bayesian
artificial neural networks.

Both GALEX and FIMS did not cover the whole sky; the whole region around the
Galactic plane and bright stars were not observed by GALEX, while several
hollow areas corresponding to the orbits with a power problem exist in the
FIMS dataset. Our objective in this study is to fill the unsurveyed regions of
the FIMS map for the total FUV intensity of the FIMS L-band, using all sky
surveys completed at other wavelengths and a deep learning algorithm. We use
the FIMS dataset for this supervised learning because the high-intensity
Galactic plane is missing in the GALEX dataset, while FIMS covers both low and
high-intensity regions. As it is difficult to confirm the validity of the
predicted FUV intensities of the unsurveyed regions due to lack of
observations in the corresponding wavelengths, we do not intend to furnish a
precise map, but rather present a reasonable map of a global scale constructed
with the assistance of recently-developed neural network techniques.
Nevertheless, indirect validation is possible by comparing the map with
simulations of dust scattering in FUV which have often been used to model the
interstellar dust, as well as with the H$\alpha$ map which is similar to the
diffuse FUV map after extinction correction in both wavelengths. Another
objective of our study is to demonstrate the utility of machine learning in
astrophysics: The present work shows that a very simple deep learning
algorithm produces remarkable results from unbiased databases even without
imposing any a priori assumptions based on experience. The present paper is
organized as follows: Section 2 delineates the construction of the FUV all sky
map from the incomplete FIMS data. We first outline the structure of the FIMS
data, followed by the detailed description of the DNN algorithm. The resulting
map is presented and compared with GALEX observations. In Section 3, we apply
dust scattering simulations to verify the validity of the predicted FUV
intensities. We conclude the paper with a summary in Section 4.

##  2 Construction of FUV the all sky map

###  2.1 Datasets

FIMS data that covers only $\sim$75 % of the sky (Seon et al., 2011a) were
stored using the HEALPix scheme (Gorski et al., 2005) with a resolution
parameter of Nside=512, corresponding to $\sim$7′. The diffuse emission
map111https://drive.google.com/file/d/1ZO_3n7-aUijxLUJA1auhL2l18fRCVars/view?usp=sharing
of the FIMS L-band was constructed from this archival data with a resolution
parameter of Nside=64 (corresponding to $\sim$1°), after the bright pixels
corresponding to bright stars had been removed (Jo et al., 2017). The angular
resolution of $\sim$1°, which is much lower than the original archival
dataset, was selected to secure the minimum signal-to-noise ratio to be above
5 even for the faintest pixel of $\sim$200 CU. With this resolution, the
entire sky consisted of 49,152 total spatial pixels, 37,152 of which had non-
zero values obtained by FIMS and 12,000 of which were empty. Fig. 1 shows the
FIMS diffuse FUV emission map of the L-band with a resolution of $\sim$1°.

Figure 1: All sky maps utilized in the study: (a) FUV observed by FIMS, (b)
H$\alpha$, (c) E(B-V), (d) N(HI), (e) soft X-ray R2 band of ROSAT, and (f)
soft X-ray R5 band of ROSAT.

To estimate the FUV intensities for regions not covered by FIMS, the following
survey data obtained for other wavelengths were used as input data throughout
the training, validation, and prediction stages: A composite H$\alpha$
map222https://lambda.gsfc.nasa.gov/data/foregrounds/halpha/lambda_halpha_fwhm06_0512.fits
of Finkbeiner (2003); E(B-V)
map333https://lambda.gsfc.nasa.gov/data/foregrounds/SFD/lambda_sfd_ebv.fits of
Galactic reddening by Schlegel, Finkbeiner & Davis (1998); neutral hydrogen
column density N(HI)
map444https://lambda.gsfc.nasa.gov/data/foregrounds/combined_nh/lambda_combined_nh.fits
of Dickey & Lockman (1990); R2 (1/4 keV) and R5 (3/4 keV) band
maps555http://www.jb.man.ac.uk/research/cosmos/rosat/RASS_SXRB_R2.fits,666http://www.jb.man.ac.uk/research/cosmos/rosat/RASS_SXRB_R5.fits
of the ROSAT constructed by Snowden et al. (1997). These survey maps are the
representative ones ranging from X-ray to radio wavelengths. They trace
different ISM phases according to their physical emission mechanism (X-ray
originating from hot gas with T $\sim$ 106 K, H$\alpha$ from photoionized gas
with T $\sim$ 104 K, E(B-V) tracing dust extinction, and N(HI) tracing the
neutral atomic hydrogen gas) and show their own distinct shapes, as depicted
in Fig. 1. We used two X-ray bands because the all-sky maps constructed from
these two bands are quite different from each other; the R2 band shows a
striking negative correlation with the neutral ISM while the R5 band has an
overall positive correlation. We did not attempt to give weights to particular
wavelengths as such a biased action reflects our prejudice regarding the
detailed emission and extinction physics that depends on wavelengths and
varies from region to region, which we are not certain about. We rather left
the deep learning algorithm to find out the nonlinear relationships between
the FUV intensities and those of other wavelengths. The acquired nonlinear
relationship in the learning stage is verified at the validation stage, in
which the predicted results are compared with the observed data which were not
used in the learning stage. All maps, although they may have high signal-to-
noise ratios at higher resolution, were binned to match the resolution of FIMS
because the deep learning algorithm requires the input datasets to have pixel-
to-pixel correspondence for direct comparisons. Galactic longitudes and
latitudes were also employed as input data to account for the spatial
variations in the relationship between the input datasets.

We randomly selected 70% of the 37,152 pixels with non-zero values for
training, while the remaining 30% were used for validation. As each dataset
has its own scales that differ from each other by several orders of magnitude,
before applying the DNN algorithm we adjusted the dataset ranges by taking
logarithmic values and normalizing them such that all final datasets have a
zero mean with a standard deviation of 1. This normalization process is
necessary because the difference in intensity among the observed datasets is
enormous in the present work, by a factor of up to 1021. Unscaled input
variables may lead to slow or unstable learning, often causing the learning
process to fail (Sola & Sevilla, 1997). Therefore, it is a general practice to
normalize the input data to have the same dispersions to guarantee
convergence. Furthermore, the log-scale normalization process also accords
well with the log-normal property found in the ISM density distribution
(Ostriker, Stone & Gammie, 2001; Seon, 2012; Burkhart et al., 2015). The
predicted FUV intensities were finally obtained by applying the inverse of the
normalization process .

Figure 2: Architecture of the neural network adopted in the present study
Figure 3: Combined map of the observed and predicted FIMS intensities.

###  2.2 Algorithm

The neural network (NN) generally consists of an input layer for input data, a
number of hidden layers for processing and learning, and an output layer. As
described in Section 2.1, we split the dataset into training and cross-
validation sets before training the model. In the training stage, weights were
applied to all input data through a series of layers, and finally the
predicted values in the output layer were compared to the target values
through a loss function. For the input data, we chose seven datasets, five of
which were the observed maps of H$\alpha$, E(B-V), N(HI), and two X-ray bands,
and the remaining two corresponds to Galactic longitudes and latitudes, as
described in Section 2.1. The FIMS FUV intensities were regarded as the
training target parameters.

We adopted a simple four-layer neural network architecture that consists of
three convolution layers and one dense layer at the end, as illustrated in
Fig. 2. The model has seven input parameters and 16 neurons in every hidden
layer; the final dense layer has one predicted output value. For the
activation functions, which feature a nonlinear relationship between the input
and target datasets, we used a hyperbolic tangent (Nwankpa et al., 2018) for
the first layer and a leaky ReLU (Maas, Hannun & Ng, 2013) for the second and
the third layers. A hyperbolic tangent is a saturated activation function that
generates saturated values for large input parameter values, while the leaky
ReLU is non-saturated neurons that provide large output values for large input
parameters, and small negative slope instead of being zero when input < 0\. We
tried several other activation function combinations, but the chosen one
provided the best results. We employed a dropout layer after each convolution
layer during the training stage to improve errors and reduce overfitting
(Srivastava et al., 2014). The dropout rates were 0.03, 0.03, and 0.05 for the
respective three layers. The present study adopted Keras 2.3.1 library and
TensorFlow 1.14.0 as a backend framework (Chollet et al., 2015).

Internal learnable parameters such as weights and biases were updated using
RMSprop (Hinton et al., 2012), an optimization algorithm that utilizes the
root mean square of the recent gradients for each weight, with a learning rate
of 10-4. A random uniform function was adopted for initial weights because
completely random initial weights may impair the final predicted values.
During the training stage, predicted FUV intensities were compared to observed
FIMS values through a loss function that evaluated numerical distances between
estimated and actual values. In our model, we used the mean-squared-error
(MSE) loss function. Our network was trained with 103 update iterations and
the final loss value was 0.11. Training data and codes can be downloaded via
the GitHub link of “https://github.com/yjchoi83/FIMS_FUV”. FIMS data were
compared with GALEX data to confirm the reliability of the final predicted
FIMS data. Confirmation tests are described in Section 2.3.

###  2.3 FUV all sky map

Fig. 3 shows a combined map of the original observed FIMS data and the
predicted FIMS FUV intensities filled in for the unsurveyed regions. It is
remarkable that the predicted regions are largely indistinguishable from the
observed regions, although the features in the predicted regions (e.g., in the
northern region of l = 150°) are smoother than those in the observed regions.
Some bright regions in and around the Galactic plane are evident; for example,
the region of (l, b) $\simeq$ (-50°, 0°) corresponds to the Lower Centaurus
Crux (the nearest OB association), and the region of (-180°< l < -120°, -30°<
b < 0°) corresponds to the upper part of the Orion-Eridanus Superbubble that
includes Orion nebula, Barnard’s loop, and Lambda Orionis.

Figure 4: Comparison of the observed and predicted FIMS intensities with GALEX
intensities. Black (red) dots represent the observed (predicted) FIMS data.
The number of pixels and correlation coefficients estimated using the
logarithmic scale are displayed in the upper-left and lower-right corners
using the corresponding color notation. Figure 5: Histogram of the difference
between FIMS and GALEX intensities. Black and red histograms correspond to the
observed and predicted FIMS data, respectively. Both histograms are fitted
using Gaussian curves with centers and widths indicated.

In Fig. 4, we compare observed (black) and predicted (red) FIMS intensities
with the GALEX observations. Overall, there is a good linear relationship
between both the observed and predicted FIMS intensities with the GALEX
observations, although the observed FIMS data are somewhat scattered toward
higher intensities than the corresponding GALEX data, which resulted in
slightly higher predicted intensities. On the other hand, at high intensities
the GALEX observations are a little brighter than FIMS. The correlation
coefficient estimated using the logarithmic scale exceeds 0.9 for the observed
and predicted cases.

Fig. 5 displays a histogram of the difference between the FIMS and GALEX
intensities ((IFIMS-IGALEX)/(IFIMS+IGALEX)). Black and red histograms
correspond to the observed and predicted FIMS data, respectively. Overall,
both histograms are well fitted to single Gaussian functions overlaid using
dashed lines. Compared to the fitted Gaussian function, the black histogram
shows excess on the right-hand side of Fig. 5, implying that the observed FIMS
intensities are somewhat brighter than the GALEX intensities. This corresponds
to the spread of the observed FIMS data toward higher intensities compared to
the GALEX data (Fig. 4). These differences are caused by instrumental
scattering of bright stellar photons by the slit (see Jo et al., 2016, Figure
1). Unlike the observed FIMS data, the predicted FIMS intensities do not
exhibit such excess.

Figure 6:  Comparison of the observed and predicted intensities for the
Galactic low latitude region of 10$\degr$ < l < 20$\degr$, |b| < 20$\degr$:
(a) actual FIMS observation, (b) predicted result, and (c) scatter plot of the
predicted intensities compared with the actual observation.

Figure 7: Comparison of the observed (black dots) and predicted (red dots)
FIMS intensities with H$\alpha$ intensities for the Galactic plane region of
|b|<30°. Left and right figures show the scatter plots before and after
extinction-correction, respectively.  Figure 8: Histograms of I${}_{\rm
FUV}\times\sin$|b| using a logarithmic scale: Black and red histograms
correspond to the observed and the predicted FIMS intensities, respectively.
Both histograms are fitted with Gaussian curves, with centers and widths
indicated.

The comparison shown in Figs. 4 and 5 were made only for the regions that were
observed by the GALEX. Therefore, we attempted to ensure the validity of the
predicted FUV intensities for the bright Galactic plane region, which GALEX
did not observe, by employing the following test. We selected a small region
of 10$\degr$ < l < 20$\degr$, |b| < 20$\degr$ around the Galactic plane, which
FIMS had observed except the lower left corner, and applied the same DNN
algorithm to the whole sky with this region intentionally excluded in the
learning process. The predicted result for this region was then compared with
the actual FIMS observation. Fig 6 shows the comparison: (a) actual FIMS
observation, (b) predicted result, and (c) scatter plot of the predicted
intensities compared with the actual observation. As can be seen from the
plots, the observed and predicted results are in good agreement, with the
correlation coefficient of 0.844 and the mean difference of 17.4$\%$. Though
these numbers do not guarantee the reliability of the predicted intensities of
the Galactic plane region, we note that the estimated error of FIMS is
$\sim$25$\%$ (Edelstein et al., 2006b).

Further, we compared the FUV intensities with those of H$\alpha$ for the
Galactic low latitude region, because previous studies showed they exhibited a
good correlation in the halo region (Seon et al., 2011b). For the Galactic
plane region, where extinction effect is severe, we applied the following
simple formula for extinction (Natta & Panagia, 1984; Castelli, Kinney &
Storchi-Bergmann, 1994; Bennett et al., 2003) with assumption that photon
sources and scattering dust grains are uniformly mixed in a plane parallel
medium:

$I_{extinction-corrected}=I_{observed}\times\frac{\tau}{1-e^{-\tau}},$ (1)

where the optical depth $\tau$ was chosen to be 7.3$\times$E(B-V) for FUV and
2.2$\times$E(B-V) for H$\alpha$ according to the Milky Way dust extinction
curve. The correction result was not significantly affected by how the
scattering effect was treated (no scattering, perfect forward scattering, and
isotropic scattering). Fig. 7 shows the observed and predicted FIMS
intensities plotted against the H$\alpha$ intensities for the Galactic plane
region of |b| < 30°. The panel on the left is the one before extinction
correction. It is apparent that the predicted data points (red dots) closely
follow the trends of the observed data points (black dots). Though the data
points are widely dispersed, the FIMS FUV intensities correlate strongly with
H$\alpha$ intensities for H$\alpha$ intensities less than $\sim$10 R. Above 10
R, FIMS FUV intensities exhibit more extinction than those of visible
H$\alpha$. In fact, infrared emission observed at 100 $\mu$m is also bright in
this section of the high intensities (Seon et al., 2011b). The panel on the
right is the one with extinction correction, based on the above simple
formula. We can see good linear relationship between the FUV and H$\alpha$
intensities, regardless of the level of their intensities. We also note that
the observed data points are less dispersed after extinction correction.

The histograms depicted in Fig. 8 confirm the validity of the predicted FIMS
results. The black and red histograms in Fig. 8 correspond to the observed and
predicted FIMS intensities multiplied by $\sin$|b|, respectively. Seon et al.
(2011a) detailed the log-normal property of the diffuse FUV intensity
distribution and interpreted it as a natural consequence of the density
structure and turbulence property of the ISM. Fig. 8 shows that the log-normal
property is well preserved for the predicted FIMS intensities. While the
centers of the two histograms are nearly collocated, the predicted FIMS
histogram width is smaller than that of the observed FIMS data, indicating
that predicted intensities fluctuate less than the observed ones.

Figure 9: (a) Combined map of the observed FIMS data and the predicted FUV
intensities. White contours indicate the boundaries between the observed and
predicted data. The large central and small lower-right regions are the
observed areas, whereas the upper-left corner and the strip on the lower-right
corner are the predicted areas; (b) dust scattering simulation map
corresponding to the entire region shown in (a).

##  3 Discussion: Dust scattering simulation

The diffuse continuum background, known as the diffuse Galactic light, comes
primarily from starlight scattered by interstellar dust. Here, we use dust
scattering simulation results to test the reliability of the DNN-predicted FUV
intensities. We selected a relatively large region spanning more than
50$\degr$ in the longitude and latitude directions, centered at (l, b) =
(175°, -30°), including both observed and predicted regions (Fig. 9a). The
observed and predicted regions were separated by the white boundaries; the
large central region with conspicuous pixel-to-pixel fluctuations is the
observed region, and most of the outer regions with smooth intensity are the
predicted regions. Dust scattering simulations for the FIMS observations have
been reported for two parts of the region shown in the figure, namely the
Orion-Eridanus Superbubble (Jo et al., 2012) at the lower left region and the
Taurus-Perseus-Auriga Complex (Lim, Min & Seon, 2013) at the upper right
region. The upper left region is Lambda Orionis, analyzed in Lee, Seon & Jo
(2015) using the data observed by the S2/68 UV telescope (Boksenberg et al.,
1973); neither FIMS nor GALEX observed the region. The faint lower right
region was observed with GALEX but not with FIMS.

For the simulation’s dust distribution, we combined the three recent 3D dust
maps of Lallement et al. (2019)777Stilism (https://stilism.obspm.fr/ or
http://cdsarc.u-strasbg.fr/viz-bin/cat/J/A+A/625/A135), Green et al.
(2019)888Bayestar19 (http://argonaut.skymaps.info/), and Leike & Enßlin
(2019)999Galactic dust absorption maps (https://wwwmpa.mpa-
garching.mpg.de/$\sim$ensslin/research/data/dust.html) to build a 3D dust map
up to a distance of $\sim$2 kpc from the Sun. We took a rectangular box of
800$\times$800$\times$400 cells, with a bin size of 5 pc. Each bin was
assigned an extinction density corresponding to the E(B-V) values for 5
parsecs from the E(B-V) value per parsec. Radiation sources were adopted from
the TD-1 (Thompson et al., 1978) and Hipparcos (Perryman et al., 1997)
catalogs. The TD-1 catalog provided the observed FUV band fluxes at
$\lambda$1565Å, which were then converted to intrinsic luminosities after an
extinction correction using updated distances. The Hipparcos catalog provided
only the spectral types; therefore, we derived stellar luminosities for the
Hipparcos stars using Castelli’s stellar models (Castelli & Kurucz, 2003) and
estimated the FUV fluxes from the stellar luminosities. Distances to the stars
were obtained from the GAIA DR2 (Gaia Collaboration, 2016, 2018) and Hipparcos
catalogs.

Optical properties of dust grains can differ based on line-of-sight and
distance. However, previous studies showed that they were similar in the
Orion-Eridanus Superbubble and the Taurus-Perseus-Auriga Complex regions with
(albedo, g-factor) = ($0.43_{-0.04}^{+0.02}$, $0.45_{-0.2}^{+0.2}$) for the
Orion-Eridanus Superbubble region (Jo et al., 2012) and
($0.42_{-0.05}^{+0.05}$, $0.47_{-0.27}^{+0.11}$) for the Taurus-Perseus-Auriga
Complex region (Lim, Min & Seon, 2013). Therefore, we adopted (albedo,
g-factor) = (0.43, 0.45) for our study. A total of 1010 stellar photons were
used in this simulation.

Figure 10: Comparison of the FIMS and dust scattering model intensities. Black
and red dots correspond to the observed and predicted data, respectively.
Figure 11: Histogram of differences between the FIMS and the dust scattering
model intensities. Black and red histograms correspond to the observed and
predicted FIMS data, respectively. Both histograms are fitted with Gaussian
curves, with centers and widths indicated.

Fig. 9(b) shows simulation results (henceforth the model map) using the same
pixel size and color scheme as in Fig. 9(a). The model map exhibits good
agreement with the combined map, although the simulation map is smoother in
part due to lower resolution of the 3D dust map. Furthermore, the overall
intensity variation is larger in the model map than in the combined map,
possibly because the model dust map has extinction densities lower than their
actual values and no high enough spatial resolution to represent the complex
density variation of dust clouds. In fact, the extinction density up to 100 pc
from the Sun is much smaller in the 3D dust map of Leike & Enßlin (2019) than
in other maps, which lowers the dust-scattered intensity. It is also known
that a clumpy medium has a lower effective optical-depth compared to a
homogeneous medium with the same dust mass and yields a lower scattered light
in high-intensity regions and a higher scattered light in low-intensity
regions (e.g., Seon & Witt, 2013; Seon & Draine, 2016). The excess of the
model intensity in high-intensity regions is likely to be attributable to both
effects. The expectation in a clumpy medium explains the general trend shown
in Fig. 9 very well. We also note that Lee, Seon & Jo (2015) obtained slightly
different albedo and g-factor of $(0.31^{+0.03}_{-0.03},0.65^{+0.06}_{-0.06})$
using a shell + ring model, which cannot be represented with a 5-pc spatial
resolution, for the Lambda Orionis nebula. This difference stresses the
importance of accurate knowledge of the 3D dust density.

The simulation model’s validity is further analyzed in Fig. 10, in which the
FIMS observation and prediction pixels are compared with those of the
simulation. In addition, Fig. 11 shows two histograms of the differences
between the observed/predicted intensities and the dust scattering simulations
((IFIMS-IModel)/(IFIMS+IModel)). It is impressive that the 0.96 correlation
coefficient for the predicted data is larger than the coefficient 0.80 for the
observed data. The higher correlation coefficient for the predicted map may be
due to its smaller pixel-to-pixel statistical fluctuations. Both the observed
and predicted maps exhibit $\sim$300 CU higher intensities than the model
simulation map in the low intensity region of < $\sim$1000 CU. This $\sim$300
CU excess may be due to extragalactic background emission (Gardner et al.,
2000; Brown et al., 2000), and/or an inaccurate representation of the detailed
density structure in the 3D dust map. Fig. 11 also indicates high confidence
in the predicted FIMS intensities. The statistical deviations of the
simulation results from the model values have similar Gaussian distributions
for both the observed and the predicted regions. Consequently, the dust
scattering simulation well reproduces the overall feature of the observed and
DNN-predicted FIMS data. This result suggests that the DNN algorithm provides
a reasonably good prediction for unsurveyed FUV sky map.

##  4 Summary

In this study, a deep learning algorithm was applied to fill unsurveyed
regions of the FUV all sky survey and a combined map was constructed based on
the observed and predicted intensities for the whole sky map. The all sky maps
of H$\alpha$, E(B-V), N(HI), and two X-ray bands, together with Galactic
longitudes and latitudes, were employed as input parameters while the
incomplete FUV intensity map made by FIMS was a target parameter. Even with a
simple four-layer neural network architecture that consisted of three
convolution layers and a final dense layer, results were remarkably consistent
with other observations. To test the validity and usefulness of the predicted
intensities further, a small region of the combined map, including both the
observed and the predicted regions, was compared to the dust scattering
simulation model that utilized recent 3-D Galactic dust maps and star catalogs
(e.g., TD-1 and Hipparcos). Simulation results exhibited good agreement with
the combined FUV map in the observed and predicted regions.

Whereas the predicted FUV intensities need to be confirmed by direct
observations, the present combined map could be a starting point for studies
that involve the FUV continuum emissions. This includes the
extinction/scattering studies for interstellar clouds, as illustrated in
Section 3. The FUV all sky map also provides important clues to the radiation
transfer mechanisms on a global scale, especially when used together with the
global maps in other wavelengths. Further, the optically thick and complex
Galactic low latitude regions are interesting and challenging in view of deep
learning. Finally, we note here that the final combined map, based on the
HEALPix scheme with an angular resolution of Nside = 64, can be downloaded
from the
website101010https://drive.google.com/file/d/1841qiiVj4E49kZFkNU3aAhvbbZ3qxMBM/view?usp=sharing.

## Data Availability

The data underlying this article are available in the GitHub link of
“https://github.com/yjchoi83/FIMS_FUV”.

## Acknowledgements

This research was supported by the Korea Astronomy and Space Science Institute
under the R&D program supervised by the Ministry of Science, ICT, and Future
Planning of Korea. Support was also provided by the Basic Science Research
Program through the National Research Foundation of Korea (NRF), funded by the
Ministry of Education (2019R1F1A1061102).

## References

  * Akshaya et al. (2018) Akshaya M. S., Murthy J., Ravichandran S., Henry R. C., Oerduin J., 2018, ApJ, 858, 101
  * Akshaya et al. (2019) Akshaya M. S., Murthy J., Ravichandran S., Henry R. C., Oerduin J., 2019, MNRAS, 489, 1120
  * Ball & Brunner (2010) Ball N. M., Brunner R. J., 2010, Int. J. Modern Phys. D, 19, 1049
  * Baron (2019) Baron D., 2019, preprint (arXiv: 1904.07248v1)
  * Bennett et al. (2003) Bennett C. L. et al., 2003, ApJS, 148, 97
  * Boksenberg et al. (1973) Boksenberg A. et al., 1973, MNRAS, 163, 291
  * Brown et al. (2000) Brown T. M. et al. 2000, AJ, 120, 1153
  * Burkhart et al. (2015) Burkhart B., Lee M. Y., Murray C. E., Stanimirović S., 2015, ApJ, 811, L28
  * Castelli, Kinney & Storchi-Bergmann (1994) Calzetti D., Kinney A. L., Storchi-Bergmann T., 1994, ApJ, 429, 582
  * Castelli & Kurucz (2003) Castelli F., Kurucz R. L., 2003, in Piskunov N., Weiss W. W., Gray D. F., eds, Proc. IAU Symp. 210, Modelling of Stellar Atmospheres. Astron. Soc. Pac., San Francisco, p. A20
  * Choi et al. (2013) Choi Y. J. et al., 2013, ApJ, 774, 34
  * Choi et al. (2015) Choi Y. J. et al., 2015, ApJ, 800,132
  * Chollet et al. (2015) Chollet F. et al., 2015, https://keras.io
  * Das & Sanders (2019) Das P., Sanders J. L., 2019, MNRAS, 484, 294
  * Davies, Serjeant & Bromley (2019) Davies A., Serjeant S., Bromley J. M., 2019, MNRAS, 487, 5263
  * Dickey & Lockman (1990) Dickey J. M., Lockman F. J., 1990, A&ARv, 28, 215
  * Draine (2003) Draine B. T., 2003, ApJ, 598, 1017
  * Edelstein et al. (2006a) Edelstein J. et al., 2006a, ApJ, 644, L153
  * Edelstein et al. (2006b) Edelstein J. et al., 2006b, ApJ, 644, L159
  * Finkbeiner (2003) Finkbeiner D. P., 2003, ApJS, 146, 407
  * Gaia Collaboration (2016) Gaia Collaboration, Brown A. G. A. et al., 2016, A&A, 595, A2
  * Gaia Collaboration (2018) Gaia Collaboration, Brown A. G. A. et al., 2018, A&A, 616, A1
  * Gardner et al. (2000) Gardner J. P. et al. 2000, ApJ, 542, L79
  * Gorski et al. (2005) Gorski K. M. et al., 2005, ApJ, 622, 759
  * Green et al. (2019) Green G. M. et al., 2019, preprint (arXiv:1905.02734)
  * Henry (2012) Henry R. C. 2012, MmSAI, 83, 409
  * Henry et al. (2015) Henry R. C., Murthy J., Overduin J., Tyler J. 2015, ApJ,798, 14
  * Hinton et al. (2012) Hinton et al., 2012, preprint (arXiv:1207.0580v1)
  * Jo et al. (2012) Jo et al., 2012, ApJ, 756, 38
  * Jo et al. (2016) Jo et al., 2016, MNRAS, 456, 417
  * Jo et al. (2017) Jo et al., 2017, ApJS, 232, 21
  * Jo et al. (2019) Jo et al., 2019, ApJS, 243, 9
  * Jyothy et al. (2015) Jyothy S. N., Murthy J., Karuppath N., Sujatha N. V. 2015, MNRAS, 454, 1778
  * Kim & Brunner (2017) Kim E. J., Brunner R. J., 2017, MNRAS464, 4463
  * Kovács & Szapudi (2015) Kovács A., Szapudi I., 2015, MNRAS, 448, 1305
  * Lallement et al. (2019) Lallement R. et al., 2019, A&A, 625, A135
  * LeCun, Bengio & Hinton (2015) LeCun Y., Bengio Y., Hinton G., 2015, Nature, 521, 436
  * Lee, Seon & Jo (2015) Lee D., Seon K. I., Jo Y. S., 2015, ApJ, 806, 274
  * Leike & Enßlin (2019) Leike R. H., Enßlin T. A., 2019, A&A, 631, A32
  * Lim, Min & Seon (2013) Lim T. H., Min K. W., Seon K. I., 2013, ApJ, 765, 107
  * Lipton, Berkowitz & Elkan (2015) Lipton Z. C., Berkowitz J., Elkan C., 2015, preprint (arXiv:1506.00019v4)
  * Martin et al. (2003) Martin C. et al., 2003, SPIE Conf. 4854, The Galaxy Evolution Explorer. Future EUV/UV and Visible Space Astrophysics Missions and Instrumentation
  * Maas, Hannun & Ng (2013) Maas A. L., Hannun A. Y., Ng A. Y., 2013, Proc. ICML, 30, 3
  * Morrissey et al. (2007) Morrissey P. et al., 2007, ApJS, 173, 682
  * Murthy, Henry & Sujatha (2010) Murthy J., Henry R. C., Sujatha N. V. 2010, ApJ, 724, 1389
  * Murthy (2014a) Murthy J. 2014a, ApJS, 213, 32
  * Murthy (2014b) Murthy J. 2014b, Ap&SS, 349, 165
  * Murthy (2016) Murthy J. 2016, MNRAS, 459, 1710
  * Narayan, Murthy & Karuppath (2017) Narayan S., Murthy J., Karuppath N. 2017, MNRAS, 466, 3199
  * Natta & Panagia (1984) Natta A., Panagia N., 1984, ApJ, 287, 228
  * Naul et al. (2018) Naul et al., 2018, NatureAstronomy, 2, 151
  * Nwankpa et al. (2018) Nwankpa C. et al., 2018, preprint (arXiv:1811.03378)
  * Ostriker, Stone & Gammie (2001) Ostriker E. C., Stone J. M., Gammie C. F., 2001, ApJ, 546, 980
  * Pashchenko, Sokolovsky & Gavras (2018) Pashchenko I. N., Sokolovsky K. V., Gavras P., 2018, MNRAS, 475, 2326
  * Pasquet et al. (2019) Pasquet J. et al., 2019, A&A, 621, A26
  * Perryman et al. (1997) Perryman M. A. C. et al., 1997, A&A, 323, L49
  * Rawat & Wang (2017) Rawat W., Wang Z., 2017, Neural Computation, 29(9), 2352
  * Schaefer et al. (2018) Schaefer C. et al., 2018, A&A, 611, A2
  * Schlegel, Finkbeiner & Davis (1998) Schlegel D. J., Finkbeiner D. P., Davis M., 1998, ApJ, 500, 525
  * Seon et al. (2011a) Seon K. I. et al., 2011a. ApJS, 196, 15
  * Seon et al. (2011b) Seon K. I. et al., 2011b, ApJ, 743, 188
  * Seon (2012) Seon K. I. 2012, ApJ, 761, L17
  * Seon & Witt (2013) Seon K. I., Witt A. N., 2013, ApJ, 778, 40
  * Seon & Draine (2016) Seon K. I., Draine B. T., 2016, ApJ, 833, 201
  * Snowden et al. (1997) Snowden S. L. et al., 1997, ApJ, 485, 125
  * Sola & Sevilla (1997) Sola J., Sevilla J., 1997, IEEE Transactions on Nuclear Science, 44, 1464
  * Srivastava et al. (2014) Srivastava N. et al., 2014, JMLR, 15, 1929
  * Thompson et al. (1978) Thompson G. I. et al., 1978, Catalogue of Stellar Ultraviolet Fluxes. A Compilation of Absolute Stellar Fluxes Measured by the Sky Survey Telescope (S2/68) Aboard the ESRO Satellite TD-1. Science Research Council, London

##  Appendix A Test of the impact of an unreasonable input dataset

We argued in the main text that the final prediction map in Fig. 3 is
reasonable through various tests. However, it should be noted that successful
prediction depends on a proper choice of input datasets; however, they can
also be arbitrary. One trivial question in this line is, how would a totally
irrelevant input dataset affect the result? To answer this question, we tested
the impact of an unreasonable input dataset with a geoid height
map111111https://earth-info.nga.mil/GandG/wgs84/gravitymod/egm96/egm96.html,
which has nothing to do with the present FUV study. We took the geoid height
map, shown in Fig. 12a, as the eighth input dataset and ran the same DNN code,
along with the seven original datasets. The result is shown in Fig. 12b, which
is hardly different from the original result in Fig. 3. We also compared the
predicted FUV intensities with the corresponding GALEX observations in Fig.
12c and obtained a result very similar to that shown in Fig. 4. We believe
that this test confirms that an irrelevant dataset would not contribute to the
final result, implying that the input datasets adopted in this study
contribute to the final predicted FUV map with appropriate weights.

Figure 12: (a) Geoid height map (NGA/NASA EGM96, N=M=360 Earth Gravitational
Model), adopted as the eighth input dataset to test the impact of an
irrelevant input, (b) combined map of the resulting FUV predictions and the
observations, corresponding to Fig. 3, and (c) comparison of the observed and
predicted FIMS intensities with GALEX intensities, corresponding to Fig. 4.