[a,b]Mario Bertaina

# Machine Learning for Mini-EUSO Telescope Data Analysis

Mikhail Zotov  Dmitry Anzhiganov  Dario Barghini  Carl Blaksley  Antonio
Giulio Coretti  Aleksandr Kryazhenkov  Antonio Montanaro  Leonardo Olivi

###### Abstract

Neural networks as well as other methods of machine learning (ML) are known to
be highly efficient in different classification tasks, including
classification of images and videos. Mini-EUSO is a wide-field-of-view imaging
telescope that operates onboard the International Space Station since 2019
collecting data on miscellaneous processes that take place in the atmosphere
of Earth in the UV range. Here we briefly present our results on the
development of ML-based approaches for recognition and classification of
track-like signals in the Mini-EUSO data, among them meteors, space debris and
signals the light curves and kinematics of which are similar to those expected
from extensive air showers generated by ultra-high-energy cosmic rays. We show
that even simple neural networks demonstrate impressive performance in solving
these tasks.

##  1 Introduction

The JEM-EUSO (Joint Exploratory Missions for Extreme Universe Space
Observatory) collaboration is developing a program of studying ultra-high
energy cosmic rays (UHECRs) with a wide angle telescope from a low Earth orbit
[1]. The idea is based on the possibility to register fluorescence and
Cherenkov radiation in the ultraviolet (UV) range that is emitted during
development of extensive air showers generated by primary particles hitting
the atmosphere.

It was clear from the early stages of the development of the program that an
orbital instrument of this kind can also collect information about other
processes taking place in the atmosphere in the UV [2]. This was fully
confirmed by the TUS mission, which took place on board the Lomonosov
satellite in 2016–2017 [3]. These days, the Mini-EUSO telescope is being
operated on board International Space Station (ISS) as a part of an agreement
between the Italian Space Agency (Agenzia Spaziale Italiana) and Roscosmos
(Russia) with the aim of studying transient atmospheric phenomena, meteors,
searching for interstellar meteors and strange quark matter, and mapping
nocturnal emission of the atmosphere in the UV [4]. Here we briefly present
results of applying neural networks and other machine learning methods aimed
at recognition and reconstruction of track-like signals in the Mini-EUSO data.
These are tracks of meteors and space debris as well as signals of short
flashes with light curves and kinematics similar to those expected from
extensive air showers (EAS) of extreme energies. We shall call the later
signals as EAS-like.

##  2 Mini-EUSO Telescope

The Mini-EUSO telescope is equipped with two Fresnel lenses with a diameter of
25 cm each, and a focal surface (FS) composed of $6\times 6$ Hamamatsu
R11265-M64 MAPMTs. Every MAPMT has 64 pixels, thus providing 2304 pixels in
total. Each MAPMT has a BG3 UV-band glass filter. Mini-EUSO has a wide field
of view (FoV) of $44^{\circ}$$\times$$44^{\circ}$ with spatial resolution (FoV
of one pixel) equal to $6.3~{}\text{km}\times 6.3~{}\text{km}$.

Mini-EUSO collects data in three modes. The main mode of operation (D1) mode
has a time resolution of 2.5 $\mu$s. This is called a D1 gate time unit (GTU).
The next, D2 mode, records data integrated over 128 D1 GTUs. Finally, the D3
mode operates with data integrated over $128\times 128$ D1 GTUs resulting in
time resolution of 40.96 ms. The D1 and D2 modes have triggers, while data
collected in the D3 mode is recorded as a stream, the duration of which
corresponds to the time spent by the ISS at the nocturnal side of Earth. The
orbital period of the ISS equals to 92.9 minutes, with nocturnal parts taking
slightly longer than 1/3 of the period. Sessions of observations are performed
approximately twice per month. A typical session includes eight subsets of
data taken during nocturnal segments of orbits. A detailed description of the
instrument can be found in [4].

##  3 Search for meteors and space debris

Searches for meteors play an important role in the complementary JEM-EUSO
program [2]. However, recognizing a meteor track in the Mini-EUSO data is not
as trivial as one may expect. Let us look at a typical meteor track registered
by Mini-EUSO shown in Figure 1.

Figure 1: A typical meteor registered by Mini-EUSO. Top left: the meteor
signal. Top right: location of the meteor track on the FS; colors indicate
arrival time. Bottom left: the meteor signal (black curves) on the background
of other signals registered simultaneously. Bottom right: a “screenshot” of
the FS at the moment of the meteor signal peak.

Figure 1 illustrates several important features of meteor signals in the Mini-
EUSO data:

  * •

these signals have a characteristic shape resembling the probability density
function of a Gaussian distribution;

  * •

they form quasi-linear tracks on the focal surface;

  * •

the number of active pixels in meteor signals is small comparing to the
complete focal surface;

  * •

an amplitude of background (“non-meteor”) signals can be much greater than
that of meteors.

Another important thing to mention is that observations are performed on a
strongly varying background, which depends on the phase of the moon and the
area in the FoV of Mini-EUSO.

We have developed several methods based on machine learning and neural
networks to complement meteor studies based on the conventional approach.

###  3.1 Stack-CNN for Space Debris and Meteor Detection and Tracking

One of the new methods is based on a recent technique named Stack-CNN [5],
originally developed as an online trigger in a orbiting remediation system to
detect space debris.

The Stack-CNN operational procedure can be divided in a stacking procedure
used to enhance the signal over the background, and a convolutional neural
network (CNN), acting as a binary classifier. The stacking method is used to
generate a single image by summing over $n$ frames that are shifted according
to a combination of speed and direction of the space debris. If the
combination matches the real one, the stacked image is enhanced by a factor of
$\sqrt{n}$ in signal-to-noise ratio (SNR). Several combinations of speed and
directions were tested and the CNN was used as a binary classifier to
recognize a right combination from all the others. The method was tested and
trained with space debris simulations using the Mini-EUSO framework. It showed
extremely promising results, being able to detect signals with
$\mathrm{SNR}\sim 1\%$, which led to the exploration of offline applications.
See [5] for further details.

The Stack-CNN approach is extremely versatile as stacked combinations and the
number of frames can be chosen depending on the physics of the object, while
preserving the same trained neural network. Thus, the method was adapted to
meteors as they share similar physical properties of space debris, such as
apparent magnitude and speed. The adapted algorithm was tested using real data
from Mini-EUSO sessions. However, in $\sim 28$ min of data files a total of
878 false positives were found. This was due to the extremely variable
background illumination of Mini-EUSO, because as the telescope moves with the
ISS, observations also include light emissions coming from cities, clouds and
moon reflections. Thus, the Stack-CNN was reinforced with the Random Forest
(RF) method acting as a binary classifier on meteor lightcurves. The dataset
contains 1384 events from Mini-EUSO, equally distributed between meteors and
the background. An advantage of using real data is that events include both
Poissonian fluctuations and cities, which would have been difficult to
simulate. As a result, the trained architecture vastly outperformed the
baseline Stack-CNN and standard approaches without machine learning
techniques. In $\sim 28$ min of data files, the algorithm found 64 more meteor
events than the traditional trigger, with only 22 false positives being
triggered.

The architecture was further validated using meteor simulations with different
absolute magnitudes $M$. Out of 100 events of $M=+4$, 88 were detected by the
algorithm, 11 more than within the conventional approach. The algorithm
maintained a better performance even with fainter events of $M=+5$, detecting
70/100 events, 20 more than the standard approach. Finally, only 6/100 events
of $M=+6$ were triggered, thus defining the detection limit of the model.

Simulations were used also to estimate the goodness of the speed and azimuth
reconstruction of the Stack-CNN. It is worth noting that the triggered stacked
speed and direction combination is apparent since Mini-EUSO comoves with the
ISS. Thus, variables were converted to the real speed and azimuth values and
the performance of the reconstruction was estimated using the average value
and the standard deviation of the residual distribution. The residual
distribution of the azimuth showed $\mu_{\phi}=(-3\pm 4)^{\circ}$ and
$\sigma_{\phi}=(46\pm 3)^{\circ}$, whereas the speed residual distribution
showed $\mu_{v}=(0\pm 1)$ km/s and $\sigma_{v}=(17\pm 1)$ km/s. The results
indicate that there is no bias in the reconstruction, having average values
compatible with 0. However, the standard deviations are larger than expected,
which led to the exploration of other deep learning techniques for the track
reconstruction.

###  3.2 Physics-Based Model for Meteor Dynamics

The speed and direction reconstruction of meteors with the Stack-CNN algorithm
is limited by the range and number of stacking combinations. Decreasing the
former and increasing the latter could indeed yield a higher performance.
However, this would not be a definitive solution and it would require more
computational time. Thus, a new deep learning paradigm was investigated,
involving implicit neural representation and meteor kinematics.

Figure 2: Concept of Physics-Model using implicit neural representation,
inspired by [6]

Implicit neural representations, also referred to as coordinate-based
representations, are neural networks used to parameterize continuous and
differentiable signals, such as images. In this way, the signal is encoded in
the neural network parameters and it is often the only way an image could be
parameterized, as an analytical function would be impossible to derive.

In our work, the neural network performs a regression by mapping a pixel
coordinate to the Mini-EUSO video sequences of meteor tracks. The video lasts
10 GTUs, and the resolution is $11\times 11$ pixels, with the meteor track
starting at the center. Taking the architecture suggested in [6] as
inspiration, the physics dynamics has been implemented in the neural network
with a time-spatial transformation $T$ acting on two separate implicit neural
representations. The global pixel coordinates $(X,Y)$ are used as input for
the first neural representation, returning the background photon counts. Then,
the pixel coordinates are mapped by function $T$ to local reference frame
$(x,y)$ of the meteor through its kinematics. The meteor starts moving in the
first frame at pixel $(X_{0},Y_{0})$ at time $t=0$. In the following frames,
$t=1,\dots,n_{\mathrm{GTU}}$, the meteor position is determined by its
apparent speed $\tilde{v}$ [pix/GTU] in x-axis and y-axis.

$\begin{cases}T(X_{0},Y_{0},\tilde{v},\theta,t)=(X_{0}+\tilde{v}_{x}\cdot t,\
Y_{0}+\tilde{v}_{y}\cdot t),\\\
(x,y)=(X,Y)-T(X_{0},Y_{0},\tilde{v}_{x},\tilde{v}_{y},t).\end{cases}$

The local pixel depends on meteor dynamics and it is used as input in the
second implicit neural representation, making the model based on the physics
of the signal. The output of the second neural representation represents the
signal itself and is summed over the background photon counts. A visual
representation of the model is given in Figure 2. It is worth noticing also
that in this case the selected dynamics is very simple, i.e., a point-like
source moving with constant speed and direction, to start with the simplest
case and to consider the only interesting parameters.

The architecture could be further refined by defining the transformation T
with the analytical solutions [7] to the differential equations describing the
physical problem of the meteor body deceleration in the atmosphere [8].
Besides, the advantage of using implicit neural representation is that they
are independent of the input resolution. Hence, pixel coordinates are not
restricted to the $48\times 48$ grid of Mini-EUSO, and the speed and direction
reconstruction could be more accurate than other methods, such as the Stack-
CNN. The architecture we used is a multi-layer perceptron (MLP) with ReLU
activation functions. It is worth noting, however, that such an architecture
would underperform with RGB images or with higher resolution.

Other solutions would be mapping input coordinates to higher-dimensional
inputs, called Fourier features [9], or having an MLP with hidden sinusoidal
activations. These architectures are called SIRENs, see [10] for more details.
Thus, with future work involving more complex dynamics and images at a higher
resolution, these approaches could be much more efficient.

The model was trained and tested using the same meteor simulations presented
for the Stack-CNN. Then, the reconstructed apparent variables were converted
to the real speed and azimuth. The results outperformed the Stack-CNN,
decreasing the resolutions of the residual distributions by $17^{\circ}$ for
azimuth and 4 km/s for speed. A visual comparison is given in Figure 3,
showing the new model (blue) outperforming the Stack-CNN (pink). In the
future, this architecture could be further refined with a more complex meteor
kinematics and tested using also real data.

Figure 3: Reconstruction of Mini-EUSO meteor tracks. The comparison shows that
the implicit neural representation (blue) is more similar to the simulation
(yellow) than the Stack-CNN (pink)

###  3.3 Two-step Recognition of Meteor Tracks

One more approach of recognizing meteor tracks in the Mini-EUSO data was
implemented as a two-step procedure. At the first stage, a simple CNN was
employed for binary classification of 3D chunks of data in the input stream
into chunks that contain meteor tracks and all others (“non-meteors”). Input
data was arranged in the form of $8\times 8\times 48$ packets, where $8\times
8$ was the size of an area on the FS, and 48 was the number of time frames
included in every packet. The packets were created using sliding windows to
avoid signal loss. Training and testing the CNN was performed on a data set of
1068 meteors found with a conventional algorithm in the data of eight sessions
that took place from 2019-11-19 till 2020-04-01. Training was performed on any
seven sessions with the remaining session used for tests. The CNN demonstrated
the highest performance on all possible combinations of input data and
recognized properly all meteors. Preliminary results of implementing this step
were reported in [11] and will be presented in more detail elsewhere.

At the second stage, the task of image segmentation, i.e., recognition of hit
pixels was applied to chunks containing meteor signals that were selected by
the CNN. We tried several approaches: a MLP, a CNN, the RF, the K-nearest
neighbours method (KNN), logistic regression and XGBoost. The two latter
methods did not perform well, and we do not discuss them here. A comparison of
results of the other four techniques is presented in Table 1.

Table 1: The number of hit pixels with a meteor signal lost by different methods at the second stage of meteor recognition. The first line indicates the session number. The total number of hit meteor pixels in the respective data set is given in parentheses. | 5 | 6 | 7 | 8 | 11 | 12 | 13 | 14
---|---|---|---|---|---|---|---|---
| (422) | (1428) | (80) | (928) | (958) | (492) | (457) | (630)
MLP | 2 | 2 | 0 | 7 | 5 | 0 | 0 | 2
CNN | 8 | 1 | 11 | 9 | 5 | 3 | 1 | 5
RF | 34 | 37 | 20 | 58 | 53 | 38 | 28 | 60
KNN | 34 | 30 | 23 | 63 | 50 | 47 | 19 | 59

One can see that an MLP has outperformed all other tools demonstrating
accuracy $>99\%$. The MLP had a very simple structure with two hidden layers
with 96 and 64 neurons respectively. The CNN had one convolutional layer and
three fully-connected layers. The RF and the KNN methods employed the
amplitude and dispersion of the meteor peak as features (with a few other
parameters tested).

##  4 EAS-like events

The above two-stage approach of recognizing meteor tracks was also tested for
the search of EAS-like events in the D1 mode data collected with the time
resolution of $2.5~{}\mu$s. The number of such events found in the Mini-EUSO
data is too small to be used as a training data set. This made us use
simulations. The combination of the CNN and the MLP described in the previous
section demonstrated high performance though provided a big number of false
positives when applied to the real data. This suggests that a more accurate
simulation of the background is needed.

Another approach that we have tried can be called transfer learning. We have
employed the fact that the shape and kinematics of meteor signals is very
similar to those of EAS-like events even though they are evolving on totally
different time scales. In order to use the “meteor pipeline”, we changed the
way of input data arrangement to take into account that D1 records contain 128
time frames. We trained the respective neural networks on D3 data packets of
the size $8\times 8\times 64$. The trained pipeline was applied to the D1
records with every odd data frame omitted. Preliminary tests have demonstrated
that the resulting performance of this “transfered” pipeline in terms of the
number of found EAS-like events was comparable to that trained on simulated
data. Results of the study will be reported elsewhere.

## Acknowledgments

All neural networks discussed in the paper were implemented in Python with
TensorFlow, PyTorch and scikit-learn software libraries. The work of MZ, DA,
and AK was funded by grant number 22-22-00367 of the Russian Science
Foundation.

## References

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Full Authors list: The JEM-EUSO Collaboration

S. Abeff, J.H. Adams Jr.ld, D. Allardcb, P. Alldredgeld, R. Aloisioep, L.
Anchordoquile, A. Anzaloneed,eh, E. Arnoneek,el, M. Bagherilh, B. Baretcb, D.
Barghiniek,el,em, M. Battisticb,ek,el, R. Bellottiea,eb, A.A. Belovib, M.
Bertainaek,el, P.F. Bertonelf, M. Bianciottoek,el, F. Biscontiei, C.
Blaksleyfg, S. Blin-Bondilcb, K. Bolmgrenja, S. Brizlb, J. Burtonld, F.
Cafagnaea.eb, G. Cambiéei,ej, D. Campanaef, F. Capeldb, R. Carusoec,ed, M.
Casolinoei,ej,fg, C. Cassardoek,el, A. Castellinaek,em, K. Černýba, M.J.
Christllf, R. Colalilloef,eg, L. Contiei,en, G. Cottoek,el, H.J. Crawfordla,
R. Cremoniniel, A. Creusotcb, A. Cummingslm, A. de Castro Gónzalezlb, C. de la
Tailleca, R. Diesinglb, P. Dinaucourtca, A. Di Nolaeg, T. Ebisuzakifg, J.
Eserlb, F. Fenueo, S. Ferrareseek,el, G. Filippatoslc, W.W. Finchlc, F.
Flaminioeg, C. Fornaroei,en, D. Fuehnelc, C. Fuglesangja, M. Fukushimafa, S.
Gadamsettylh, D. Gardiolek,em, G.K. Garipovib, E. Gazdalh, A. Golzioel, F.
Guarinoef,eg, C. Guépinlb, A. Haungsda, T. Heibgeslc, F. Isgròef,eg, E.G.
Juddla, F. Kajinofb, I. Kanekofg, S.-W. Kimga, P.A. Klimovib, J.F.
Krizmaniclj, V. Kungellc, E. Kuznetsovld, F. López Martínezlb, D. Mandátbb, M.
Manfrinek,el, A. Marcelliej, L. Marcelliei, W. Marszałha, J.N. Matthewslg, M.
Meseef,eg, S.S. Meyerlb, J. Mimouniab, H. Miyamotoek,el,ep, Y. Mizumotofd, A.
Monacoea,eb, S. Nagatakifg, J.M. Nachtmanli, D. Naumovia, A. Neronovcb, T.
Nonakafa, T. Ogawafg, S. Ogiofa, H. Ohmorifg, A.V. Olintolb, Y. Onelli, G.
Osteriaef, A.N. Ottelh, A. Pagliaroed,eh, B. Panicoef,eg, E. Parizotcb,cc,
I.H. Parkgb, T. Paulle, M. Pechbb, F. Perfettoef, P. Picozzaei,ej, L.W.
Piotrowskihb, Z. Plebaniakei,ej, J. Posliguali, M. Pottslh, R. Preveteef,eg,
G. Prévôtcb, M. Przybylakha, E. Realiei,ej, P. Reardonld, M.H. Renoli, M.
Ricciee, O.F. Romero Matamalalh, G. Romoliei,ej, H. Sagawafa, N. Sakakifg,
O.A. Saprykinic, F. Sarazinlc, M. Satofe, P. Schovánekbb, V. Scottief,eg, S.
Selmanecb, S.A. Sharakinib, K. Shinozakiha, S. Stepanofflh, J.F. Sorianole, J.
Szabelskiha, N. Tajimafg, T. Tajimafg, Y. Takahashife, M. Takedafa, Y.
Takizawafg, S.B. Thomaslg, L.G. Tkachevia, T. Tomidafc, S. Toscanoka, M.
Traïcheaa, D. Trofimovcb,ib, K. Tsunofg, P. Vallaniaek,em, L. Valoreef,eg,
T.M. Venterslj, C. Vigoritoek,el, M. Vrabelha, S. Wadafg, J. Watts Jr.ld, L.
Wienckelc, D. Winnlk, H. Wistrandlc, I.V. Yashinib, R. Younglf, M.Yu. Zotovib.

aa Centre for Development of Advanced Technologies (CDTA), Algiers, Algeria
ab Lab. of Math. and Sub-Atomic Phys. (LPMPS), Univ. Constantine I,
Constantine, Algeria
ba Joint Laboratory of Optics, Faculty of Science, Palacký University,
Olomouc, Czech Republic
bb Institute of Physics of the Czech Academy of Sciences, Prague, Czech
Republic
ca Omega, Ecole Polytechnique, CNRS/IN2P3, Palaiseau, France
cb Université de Paris, CNRS, AstroParticule et Cosmologie, F-75013 Paris,
France
cc Institut Universitaire de France (IUF), France
da Karlsruhe Institute of Technology (KIT), Germany
db Max Planck Institute for Physics, Munich, Germany
ea Istituto Nazionale di Fisica Nucleare - Sezione di Bari, Italy
eb Università degli Studi di Bari Aldo Moro, Italy
ec Dipartimento di Fisica e Astronomia "Ettore Majorana", Università di
Catania, Italy
ed Istituto Nazionale di Fisica Nucleare - Sezione di Catania, Italy
ee Istituto Nazionale di Fisica Nucleare - Laboratori Nazionali di Frascati,
Italy
ef Istituto Nazionale di Fisica Nucleare - Sezione di Napoli, Italy
eg Università di Napoli Federico II - Dipartimento di Fisica "Ettore Pancini",
Italy
eh INAF - Istituto di Astrofisica Spaziale e Fisica Cosmica di Palermo, Italy
ei Istituto Nazionale di Fisica Nucleare - Sezione di Roma Tor Vergata, Italy
ej Università di Roma Tor Vergata - Dipartimento di Fisica, Roma, Italy
ek Istituto Nazionale di Fisica Nucleare - Sezione di Torino, Italy
el Dipartimento di Fisica, Università di Torino, Italy
em Osservatorio Astrofisico di Torino, Istituto Nazionale di Astrofisica,
Italy
en Uninettuno University, Rome, Italy
eo Agenzia Spaziale Italiana, Via del Politecnico, 00133, Roma, Italy
ep Gran Sasso Science Institute, L’Aquila, Italy
fa Institute for Cosmic Ray Research, University of Tokyo, Kashiwa, Japan
fb Konan University, Kobe, Japan
fc Shinshu University, Nagano, Japan
fd National Astronomical Observatory, Mitaka, Japan
fe Hokkaido University, Sapporo, Japan
ff Nihon University Chiyoda, Tokyo, Japan
fg RIKEN, Wako, Japan
ga Korea Astronomy and Space Science Institute
gb Sungkyunkwan University, Seoul, Republic of Korea
ha National Centre for Nuclear Research, Otwock, Poland
hb Faculty of Physics, University of Warsaw, Poland
ia Joint Institute for Nuclear Research, Dubna, Russia
ib Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University,
Russia
ic Space Regatta Consortium, Korolev, Russia
ja KTH Royal Institute of Technology, Stockholm, Sweden
ka ISDC Data Centre for Astrophysics, Versoix, Switzerland
la Space Science Laboratory, University of California, Berkeley, CA, USA
lb University of Chicago, IL, USA
lc Colorado School of Mines, Golden, CO, USA
ld University of Alabama in Huntsville, Huntsville, AL, USA
le Lehman College, City University of New York (CUNY), NY, USA
lf NASA Marshall Space Flight Center, Huntsville, AL, USA
lg University of Utah, Salt Lake City, UT, USA
lh Georgia Institute of Technology, USA
li University of Iowa, Iowa City, IA, USA
lj NASA Goddard Space Flight Center, Greenbelt, MD, USA
lk Fairfield University, Fairfield, CT, USA
ll Department of Physics and Astronomy, University of California, Irvine, USA
lm Pennsylvania State University, PA, USA