∎

e1e-mail<EMAIL_ADDRESS>e2e-mail<EMAIL_ADDRESS>e3e-mail:
<EMAIL_ADDRESS>
11institutetext:  INFN and University of Genova 22institutetext: University of
Luxembourg 33institutetext: Weizmann Institue of Science 44institutetext: New
York University 55institutetext: University of Wisconsin–Madison
66institutetext: ICEPP, University of Tokyo 77institutetext: Technical
University of Munich 88institutetext: Max Planck Institute for Physics
99institutetext: INFN and Sapienza University of Rome

# Configurable calorimeter simulation for AI applications

Francesco Armando Di Bello gen_add  Anton Charkin-Gorbulin lxm_add  Kyle
Cranmer nyu_add,uwm_add  Etienne Dreyer wis_add, e3  Sanmay Ganguly tok_add,
e1  Eilam Gross wis_add  Lukas Heinrich tum_add  Lorenzo Santi rom_add  Marumi
Kado mpi_add, rom_add  Nilotpal Kakati wis_add  Patrick Rieck nyu_add, e2
Matteo Tusoni rom_add

(Received: date / Accepted: date)

###### Abstract

A configurable calorimeter simulation for AI
(COCOA) applications is presented, based on the Geant4 toolkit and interfaced
with the Pythia event generator. This open-source project is aimed to support
the development of machine learning algorithms in high energy physics that
rely on realistic particle shower descriptions, such as reconstruction, fast
simulation, and low-level analysis. Specifications such as the granularity and
material of its nearly hermetic geometry are user-configurable. The tool is
supplemented with simple event processing including topological clustering,
jet algorithms, and a nearest-neighbors graph construction. Formatting is also
provided to visualise events using the Phoenix event display software.

##  1 Introduction

Algorithms incorporating machine learning (ML) methods are a new paradigm in
reconstruction, calibration, identification and analysis of High Energy
Physics (HEP) experimental data. In recent years, various ML architectures
have been deployed to optimize low-level tasks such as clustering,
reconstruction, fast simulation, pileup suppression and object identification
Guest:2018yhq ; hepmllivingreview . For example, ML-based fast calorimeter
simulation relies on accurate target data to train a fast conditional
generative model $p(D|T)$, where $T$ denotes the true set of stable final
state particles produced in the collision and $D$ is the set of resulting
detector hits. In particle reconstruction, on the other hand, the inverse
process $D\rightarrow T$ is modelled by predicting a set of particles $R(D)$
to approximate $T$ as accurately as possible. The development of such
algorithms requires a realistic, highly-granular simulation of particle
detector response going beyond parameterized detector models frequently used
in studies of particle physics phenomenology such as DELPHES Mertens:2015kba .
In particular due to the complexity of particle showers in calorimeters, a
detailed, microscopic simulation of interactions between particles and
detector material is needed in order to develop low-level ML algorithms
exploiting such features.

Recent research efforts to study calorimeter shower properties using ML
PhysRevD.97.014021 ; Qasim_2019 ; Di_Bello_2021  made use of the Geant4
ALLISON2016186  simulation toolkit for simple detector geometries. However an
open source simulation with a realistic cylinder like hermetic geometry and
realistic detector is yet to be adapted by HEP community for ML studies and
beyond. Aiming to bridge this gap, the COnfigurable Calorimeter simulatiOn for
Ai (COCOA) was developed, which uses Geant4 ALLISON2016186  to implement
detailed shower simulation for particles in a full-coverage, highly-segmented
sensitive volume comparable to that of multipurpose detectors at the LHC. The
program source code sanmay_ganguly_2023_7700475  is linked together with a
technical documentation on the project website111https://cocoa-
hep.readthedocs.io/en/latest/index.html. The emphasis of this software package
is on realistic calorimeter simulation. No realistic digitization and
electronic readouts are implemented and energy loss due to these processes are
neglected in this package. For the same reason, simplified tracking is
included in COCOA to model particle deflection in a magnetic field and energy
depositions upstream of the calorimeter. A sophisticated open model for
tracking suitable for tracking studies based on silicon hits is provided by
opendatadetector .

Usability for ML-based studies is a core motivation in the design of the COCOA
code. Datasets generated by COCOA have featured in two recent applications of
ML to particle reconstruction and fast simulation DiBello:2022rss ;
DiBello:2022iwf . To this end, the main parameters of the calorimeters are
largely configurable, including their material, granularity, depth and the
amount of readout noise. Similarly the inclusion of material interactions in
the tracking region is optional. For comparisons with benchmark reconstruction
approaches, output data from COCOA are conveniently interfaced to standard
topological clustering and jet clustering algorithms. The output includes a
record of energy contributions to each cell by truth particles for supervising
cell-level predictions and edge lists for connecting cells and tracks in a
graph to support geometric deep learning models. Finally, the default geometry
has been formatted for rendering in the Phoenix event display software phoenix
, along with a script to export event output files for visualization. An
example is shown in Fig. 1.

The sophisticated COCOA calorimeter simulation and its data post-processing
provides users easy access to datasets suitable to train models for current
collider experiments or for more general algorithms development and
benchmarking. On the other hand, the open-source nature of the package and its
visualization support have the potential for use cases in education and
science communication in HEP.

Figure 1: Visualization of a photon (dashed line) with energy 50 GeV
converting to two electrons (green lines) producing three distinct clusters in
the COCOA central electromagnetic calorimeter. The cluster shown in red
contains an additional cell in the first layer of the hadronic calorimeter due
to a noise fluctuation. Cells are shown with an opacity proportional to energy
over noise ratio divided by 4.6, the threshold for topoclustering seeds.

##  2 Detector design

(a)

(b)

Figure 2: Positive quadrant scheme of COCOA. We use a right-handed orthogonal
coordinate system $x$-$y$-$z$, where $z$-axis is the principal axis of the
detector and a constant $z$ refers to a circular cross-section of the
detector. (a) $yz$-projection showing the COCOA ITS, subsequent iron layers,
calorimeter system in the barrel and end-cap region, overlaid on lines marking
constant pseudorapidity $\eta$. (b) $xy$-projection shows barrel region of the
same subsystems at $z=0$. Figure 3: (left) Cumulative amounts of material, in
units of radiation length $X_{0}$ and as a function of $\eta$, in front of and
within the electromagnetic calorimeter system. (right) Cumulative amounts of
material, in units of interaction length $\lambda_{int}$ and as a function of
$\eta$, in front of and within the hadronic calorimeter system.

The major components of COCOA are an inner tracking system (ITS) surrounded by
an electromagnetic calorimeter (ECAL) and finally a hadronic calorimeter
(HCAL). These subsystems are arranged concentrically and are symmetric in
azimuthal angle $-\pi<\phi\leq\pi$ as shown in Fig. 2. No muon spectrometer is
considered in this design and muons are reconstructed as tracks with the ITS.
The goal of this design is to accurately model the relevant outputs of a
multipurpose detector at the LHC while being simplified by the exclusion of
detailed components like readout electronics, cabling, and support structures.
The detector design is largely configurable, with its default parameter values
chosen to achieve response characteristics comparable to that of the ATLAS
detector. Following is a detailed description of each subsystem.

The ITS consists of hollow cylinders in the central detector part and disks at
both of its ends, each of which are centered around the beamline. Each of
these components consists of a silicon layer of 150 µm thickness in case of
the disks and the five innermost cylinders and 320 µm in case of the 4
outermost cylinders. Each silicon layer is accompanied by an iron layer of 350
µm thickness in order to provide a simulate support material. The ITS only
serves the purpose of simulating the interaction of particles with matter
upstream of the calorimeter. The resulting detector hits are not used for
tracking purposes. The default value of the magnetic flux density present in
the ITS amounts to 3.8 T. Finally, two layers of iron totalling 4.4 cm in
depth are added to represent support or cryostat material in front of the
calorimeter.

The inner surface of the calorimeter system is a cylinder with a radius of 150
cm and a length of 6387.8 cm immediately enclosing the iron layers and the
ITS. The calorimeters are separated into a central barrel region covering the
pseudorapidity range $|\eta|<1.5$ and two end-cap regions extending the
coverage up to $\eta=3$ by default. Both the ECAL and the HCAL are divided
into 3 concentric layers, with each layer being further segmented into cells
with edges of constant $\eta$ and $\phi$. The cell granularity for each layer
is configurable by setting the number of equal divisions in $\eta$ and
(separately) $\phi$. The depth of the cells in every layer is designed to be
nearly constant in $\eta$ to ensure that the fraction of a particle’s energy
deposited in each layer does not depend on the incident angle. This design,
leading to layer shapes of the form $1\,/\,\cosh{\eta}$, provides a uniform
calorimeter thickness as a function of pseudo-rapidity. COCOA will thus have a
more uniform response than a pure circular cylindrical shape.

The COCOA calorimeter material is a compound using an equivalent molecule
approximation, mixing an absorber and scintillator material with a constant
proportion. Both the materials and their proportion can be configured for the
ECAL and the HCAL individually. By default, the ECAL is made of a mixture of
lead and liquid argon, corresponding to the ATLAS ECAL materials. The volume
proportion amounts to $1\\!:\\!3.83$, resulting in a radiation length of
$X_{0}=2.5$ cm. The ECAL and HCAL are separated by an iron layer with a
default thickness of 80 mm. The HCAL is made of a mixture of iron and
polyvinyl toluene plastic material with a volume proportion of $1.1.:1.0$,
resulting in a nuclear interaction length of $\lambda_{int}=26.6$ cm. The
integrated radiation and interaction length measured from the IP to the end of
the HCAL is shown as a function of the pseudorapidity in Fig 3.

Table 1:  Calorimeter default design values regarding layer depths in terms of radiation lengths $X_{0}$ (ECAL) and hadronic interaction lengths $\lambda_{int}$ (HCAL), granularity and energy noise levels.  Layer | Depth |  | Segmentation
---
($\eta\times\phi$)
| Std. dev. noise per cell
---
per event [MeV]
ECAL 1 |  $4\,X_{0}$ | $256\times 256$ | 13
ECAL 2 | $16\,X_{0}$ | $256\times 256$ | 34
ECAL 3 |  $2\,X_{0}$ | $128\times 128$ | 41
HCAL 1 | $1.5\,\lambda_{\mathrm{int}}$ | $64\times 64$ | 75
HCAL 2 | $4.1\,\lambda_{\mathrm{int}}$ | $64\times 64$ | 50
HCAL 3 | $1.8\,\lambda_{\mathrm{int}}$ | $32\times 32$ | 25

While this calorimeter design represents a homogeneous detector, a spread in
the resolution of reconstructed energies in accordance with a sampling
calorimeter design is emulated by means of configurable sampling fraction
parameters for the ECAL and the HCAL individually. In lieu of a complete
simulation of active and passive material, the sampling is emulated by
accounting only for a fraction of the GEANT energy deposits steps for all
particles in the calroimeter showers. The steps to removed are chosen
randomly. The sum of the total deposited energy by those steps is computed and
the total energy released is estimated by inverse scaling of the total
deposited energy by the corresponding fraction.

Noise, as for example from electronics, is simulated by the addition of random
amounts of energy following a Gaussian distribution centered around zero. The
noise is independently added to each cell. Negative energies are allowed as is
typically the case as a result from the subtraction of pedestals. If such
downward fluctuations are significant in size, those negative energy cells can
be clustered into topoclusters. The default choices of materials and smearing
parameters provided in Tab. 1 are chosen in order to approximate single-
particle responses of the ATLAS calorimeter system ATLAS:2021epk .

##  3 Data processing

Figure 4: COCOA workflow. Primary particles generated with the Pythia library
are introduced to COCOA. Their interactions with the detector material is
simulated by means of the Geant4 toolkit. Calorimeter cells identified by a
topological clustering algorithm are stored in the output ROOT file together
with true particles, emulated tracks, and particle trajectories extrapolated
from the IP through the calorimeter according to the equations of motion. A
nearest-neighbors-based graph is constructed and stored via edge lists
connecting source and destination nodes amongst the output cells and tracks.
Jets made of true particles as well as topoclusters are stored in the output
file as well. Events in the output file can be parsed for visualization in
Phoenix.

(a)

(b)

Figure 5: Number (a) and average energy (b) of reconstructed clusters in COCOA
for events with a single charged pion, electron, or photon shot at $\eta=0$.
Results are also shown for clusters reconstructed in empty events due to
electronic noise. The default topological calorimeter cell clustering settings
are used.

Every event is processed according to the workflow presented in Fig. 4. First,
primary particles are generated at the IP by means of the Pythia8 Monte Carlo
event generator pythia . A broad range of primary physics processes is
available to the user, ranging from the generation of single particles as well
as single jets up to more complicated final states with large multiplicities
of jets and leptons in the final state.

The set of final state, stable particles is stored in the output file and
passed on to the detector simulation described in the previous section, where
the propagation of these particles and their interactions with the detector
material is simulated in Geant4 ALLISON2016186 . The model of hadronic
interactions is chosen in accordance with the ATLAS and CMS detector
simulations. The sum of the energies deposited in each calorimeter cell is
stored. Electronic noise is simulated by the addition of random energy offsets
to each cell for which Tab. 1 provides the default values of standard
deviation for each layer.

For the purpose of particle reconstruction, the origin of energy deposits in
each cell is stored via a list of parent particle indices which contributed
energy into the cell and a list of weights recording their relative
contribution to the total cell energy. Cells which received their dominant
contribution from electronic noise are assigned an index of -1.

In order to limit the number of calorimeter cells stored in the output file to
a reasonable level, low-energy cells dominated by noise contributions are
suppressed using a topological clustering algorithm Aad_2017 . Only cells
contained in the resulting “topoclusters” are stored in the output file.
Topoclusters are seeded by single cells which are required to contain a
deposited energy well above the noise level, where the threshold of this
signal-to-noise ratio (SNR) is 4.6 for COCOA by default, while a value of 4.0
is used for the ATLAS experiment. This difference is chosen in order to
achieve a better agreement between ATLAS and COCOA in terms of the topocluster
multiplicity distribution for single charged and neutral pions as well as pure
noise events (Fig. 5). Starting with the seeding cells, all neighbouring cells
are added to the cluster if their SNR is above another threshold, where the
default value is set to 2. Finally, all further neighbouring cells above a
third threshold are added, which by default is set to 0. Cells with negative
energy can be included, based on their absolute value, or excluded entirely
(default configuration). Topocluster candidates containing multiple local
maxima in ECAL cell energy each surpassing 400 MeV are split into separate
topoclusters.

In order to support particle reconstruction studies which include high energy
primary photons, electron-positron pairs from photon conversions taking place
in the ITS upstream its two outermost iron layers are stored in the COCOA
output file as well. Tracks emanating from photon conversions and also primary
electron tracks are used to construct groups of topoclusters denoted
“superclusters” associated with electron and photon showers. The
superclustering procedure in COCOA follows the criteria described in
Aad2019-vd , designed to improve electron energy reconstruction by
incorporating nearby energy deposits from bremsstrahlung. It also includes
criteria for grouping multiple clusters that are related by a pair of nearby
tracks to a photon conversion vertex, thus improving reconstructed photon
energy. In the photon conversion shown in Fig. 1, for example, the COCOA
output contains a supercluster which combines the three topoclusters shown.
Due to the simplified tracking, the criteria on number of track hits are not
applied. The COCOA implementation does not focus on electron and photon
identification; rather, superclusters are only formed using tracks linked to
primary or conversion electrons.

Table 2:  Default $k$ (number of nearest-neighbors) and maximum $\Delta R$ separation used to define edges in the fixed graph creation. Edges between cells are denoted “c-c” while edges between tracks and cells are denoted “t-c”.  | ECAL layer | HCAL layer
---|---|---
| 1 | 2 | 3 | 1 | 2 | 3
$k$ (c-c) inter-layer | 1 | 2 | 2 | 2 | 2 | 1
$k$ (c-c) same layer | 8 | 8 | 8 | 6 | 6 | 6
$k$ (t-c) | 4 | 4 | 4 | 3 | 3 | 3
$\Delta R^{\mathrm{max}}$ (c-c) | 0.05 | 0.07 | 0.14 | 0.30 | 0.30 | 0.60
$\Delta R^{\mathrm{max}}$ (t-c) | 0.15 | 0.15 | 0.40 | 1.10 | 1.10 | 2.00

While the event simulation based on the Geant4 ALLISON2016186  toolkit
determines particle trajectories according to their equations of motion and
their interactions with detector material, COCOA implements a particle
tracking based only on the equations of motion for the benefit of downstream
tasks. These tracks are extrapolated to the entry surface as well as each
layer of the calorimeter and the resulting $\eta$ and $\phi$ coordinates are
stored in the output file.

For user convenience, an interface to the FastJet Cacciari_2012  library is
provided that clusters primary particles as well as topological calorimeter
cell clusters into jets. The user can choose the specific jet clustering
algorithm accordingly, with the anti-$k_{\mathrm{T}}$ algorithm set as
default.

For each event in the output data a fixed heterogeneous graph containing cells
and tracks is provided by means of two lists storing the indices of source and
destination nodes for each edge. The edges are created based on $k$ nearest
neighbors in angular distance with $k$ being user-configurable per calorimeter
layer and edge type. Three edge types are defined: track-to-cell, cell-to-cell
inter-layer, and cell-to-cell across neighboring calorimeter layers (tracks
are not directly connected). The user can configure for each of these types
both how many edges to construct in a $\Delta R$-ordered neighborhood and also
with a maximum $\Delta R$ (where $\Delta
R^{2}=\Delta\eta^{2}+\Delta\phi^{2}$). The default values are given in Tab. 2.

The final output file produced by COCOA stores an array of features for each
event which are associated with the following sets: cells that participated in
topoclusters, tracks, topoclusters, truth particles and decay record, graph
edges, and jets. The output file format is ROOT but can be converted to hdf5
format using a script provided in the repository.

Figure 6: Energy deposited by electrons, photons and charged pions for each
calorimeter layer. The electron and photon showers are limited to the
electromagnetic calorimeter (layers 1 to 3) while the charged pion showers
reach deep into the hadronic calorimeter (layers 4 to 6)

.

(a)

(b)

(c)

Figure 7: Reconstruction energies for central electrons (7(a)), photons (7(b))
and charged pions (7(c)). The average reconstructed energies follow the
initial particle energies while the energy resolution improves as the initial
particle energy increases.

##  4 Detector performance

In the following, the performance of COCOA is investigated by means of single
particles which are generated at the IP. For each particle type and momentum
under investigation, the event generation is repeated in order to gather a
statistically significant amount of events.

The correct reconstruction of particle energies is demonstrated in Fig. 5,
which compares the distributions of multiplicities (Fig. 5(a)) and energy sums
(Fig. 5(b)) of topoclusters for charged pions, photons, electrons and events
containing only noise contributions, denoted as empty events. In most of the
empty events, the cell energies do not pass the noise threshold of the
clustering algorithm. For those events in which this threshold is passed, the
average cluster energy sum amounts to 36 MeV in line with the low noise levels
provided in Tab. 1. The photons and electrons mostly result in one cluster,
while their energy is reconstructed with only a small variation. In
comparison, the charged pion events result in larger variations of the cluster
multiplicity and energy sum distributions due to the higher degree of
variations in deposited energies for the hadronic showers. The average cluster
energy sum is below the initial charged pion energy due to the involved
nuclear interactions of the shower particles with the detector material, which
are not counted as detectable energy. A hadronic calibration procedure is not
performed within COCOA but left for downstream tasks.

Patterns of energy depositions across the calorimeter are demonstrated in Fig.
6 in terms of fractions of deposited energy per calorimeter layer for
electrons, photons and charged pions. As a consequence of the material budget
presented above in Fig. 3, the electrons and photons deposit most of their
energy in the electromagnetic calorimeter, in particular in the second
calorimeter layer, while the charged pions reach the hadronic calorimeter
layers where they deposit most of their energy, in line with energy deposition
patterns at collider-detector experiments.

Figure 7 shows distributions of the reconstructed energies for central
electrons, photons and charged pions with different initial energies. The
energy resolution provided by the calorimeter response improves as the initial
particle energy increases. It is larger for charged pions compared to
electrons and photons, as expected because of the existence of large sampling
fluctuations for hadronic showers compared to electromagnetic showers.

Figure 8 shows the reconstructed energies of a single electron shot at
different initial $\eta$. The average reconstructed energy is always lower
than the initial particle energies, with the difference growing with the
particle $\eta$. This is due to the energy depositions in the iron contained
in the ITS upstream the calorimeter, in accordance with the material map
presented in Fig. 3.

Figure 9 quantifies the energy resolution as a function of particle energy,
comparing electrons with charged pions. For each particle type, the relative
energy resolution depending on the particle energy is fitted using least-
squares to the following common form of the resolution function:

$\frac{\sigma(E_{\mathrm{reco}})}{E_{\mathrm{truth}}}=\frac{a}{\sqrt{E_{\mathrm{truth}}}}\oplus\frac{b}{E_{\mathrm{truth}}}\oplus
c$ (1)

where the best-fit parameters are provided within the figure. The larger
fitted coefficient of the sampling term for hadronic shower compared to
electromagnetic is related to the larger value of sampling fraction $f$
configured for the ECAL and HCAL separately (0.07 and 0.025, respectively).
The values of the parameters, appearing in Equation 1, are individually
evaluated for photon as $a=0.16\pm 0.01$, $b=0.30\pm 0.02$ and $c=0.006\pm
0.003$. The same numbers for charged pions are found to be $a=0.50\pm 0.12$,
$b=0.32\pm 0.06$ and $c=0.086\pm 0.002$. The noise term is compatible with the
input noise values, the sampling term is as expected from the sampling
emulation.

The performance of the simulated detector has been so far probed using single
particles. To illustrate the detector performance in a more realistic event
environment $pp\rightarrow W\rightarrow e+\nu$ were simulated. The electron is
reconstructed using the superclustering algorithm described in Sec. 3, and its
energy is calibrated in order to compensate for the the loss due to scattering
in the ITS and iron layers upstream the ECAL. The missing transverse momentum
(MET) is calculated from the rescaled clusters, as the opposite the vector sum
over visible transverse momenta in the whole event. Finally the transverse $W$
mass, $m_{T}^{W}$, is computed from the reconstructed $W$ four-momentum and
compared with the corresponding truth level distribution in Fig. 10.

Figure 8: Reconstructed energies of electrons with an energy of 30 GeV for
different directions $\eta$. As the initial electron momentum is directed
closer to the beamline, the difference between the reconstructed energy and
the intial particle energy increases due to the iron traversed by the electron
upstream the calorimeter (dead material). Figure 9: The relative energy
resolution $\sigma(E_{\mathrm{reco}})/E_{\mathrm{truth}}$ is plotted as a
function of $E_{\mathrm{truth}}$ for eight different truth energy values and
fitted with the relative-resolution function, for photon and pion,
respectively. The average sampling fraction $f$ for ECAL and HCAL are shown in
the legend. Figure 10: The transverse W mass $m_{T}^{W}$ distribution is
plotted for leptonically decaying W events. The black curve shows the truth
distribution whereas the red curve is obtained from the vector sum of
reconstructed lepton momentum and the MET in the event. The peak location of
the two distributions are well aligned, demonstrating that the event-level
reconstructed MET is trustworthy within the COCOA framework.

##  5 Event display

(a)

(b)

Figure 11: Phoenix event displays configured using the COCOA detector
geometry, showing the charged particle tracks and calorimeter hits generated
by (a) $pp\rightarrow t\overline{t}$ and (b) $pp\rightarrow W\rightarrow e\nu$
events simulated with Pythia8. In (a), a cutaway of the COCOA calorimeter
volumes is shown along with the clustered cells, while in (b) only the cells
are shown. The electron from the $W$ decay in (b) is indicated by a green
line. Both displays are shown in perspective view, such that nearer objects
appear larger. Different shades of green and blue represent the different
layers of ECAL and HCAL, respectively, while cell opacity is determined by
cell signal-to-noise ratio.

Visualization of detector geometry and examples of hits for individual events
is important for communicating results, and interpreting downstream tasks such
as reconstruction and event selection. The default geometry of the COCOA
detector was ported into the open-source framework Phoenix, chosen for its
versatility and user support. An example event display is shown in Fig. 11.

##  6 Conclusion

The growing interest in ML approaches to low-level analysis tasks such as
event or jet reconstruction in a realistic detector underscores the importance
of leveraging the rich feature space of calorimeter showers for improving
these tasks. Providing an open, configurable, and realistic calorimeter
simulation, COCOA will facilitate the development of such algorithms and
ultimately expand the physics reach of current and next-generation collider
experiments. The thorough treatment of particle interactions in Geant4 and the
full-coverage, highly-granular design of COCOA calorimeter system enable an
accurate representation of the complex data environment present in the ATLAS
and CMS experiments at the LHC. To quantify this resemblance, an investigation
of the single-particle response characteristics, in terms of topological
clustering performance and energy resolution for electromagnetic and hadronic
showers, has been carried out. Finally, additional aides including data post-
processing, event visualization, and documentation for COCOA has been provided
to further encourage use.

##  7 Acknowledgments

E.G. would like to thank the United States-Israel BSF , grant NSF-BSF 2020780,
for its support. E.D. is supported by the Zuckerman STEM Leadership Program.
SG is partially supported by Institute of AI and Beyond for the University of
Tokyo. K.C. and P.R. are supported by NSF award PHY-2111244, and K.C. is also
supported by NSF award OAC-1836650. LH is supported by the Excellence Cluster
ORIGINS, which is funded by the Deutsche Forschungsgemeinschaft (DFG, German
Research Foundation) under Germany’s Excellence Strategy - EXC-2094-390783311.

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