To appear in: Artificial Intelligence for Science,

eds. A. Choudhary, G. Fox and T. Hey

Singapore: World Scientific, in press (2023)

Applications of AI in Astronomy

S. G. Djorgovski*, A. A. Mahabal*, M. J. Graham*, K. Polsterer†,

A. Krone-Martins‡

Abstract: We provide a brief, and inevitably incomplete overview of the use of

Machine Learning (ML) and other AI methods in astronomy, astrophysics, and
cosmology. Astronomy entered the big data era with the first digital sky surveys
in the early 1990s and the resulting Terascale data sets, which required automating
of many data processing and analysis tasks, for example the star-galaxy separation,
with billions of feature vectors in hundreds of dimensions. The exponential data
growth continued, with the rise of synoptic sky surveys and the Time Domain
Astronomy, with the resulting Petascale data streams and the need for a real-time
processing, classification, and decision making. A broad variety of classification
and clustering methods have been applied for these tasks, and this remains a very
active area of research. Over the past decade we have seen an exponential growth
of the astronomical literature involving a variety of ML/AI applications of an ever
increasing complexity and sophistication. ML and AI are now a standard part of
the astronomical toolkit. As the data complexity continues to increase, we
anticipate further advances leading towards a collaborative human-AI discovery.

1.1 Introduction and Background

Astronomy entered the era of big data with the advent of large digital sky surveys
in the 1990s, which opened the TB-scale regime. Sky surveys have been the
dominant source of data in astronomy ever since, reaching the multi-PB scale by
the late 2010s; see, e.g., [1] for a review. This stimulated the creation of the Virtual
Observatory (VO) framework [2,3], which has now evolved into a global data grid
of astronomy (see https://ivoa.net), providing access to data archives from both
ground-based observatories and surveys, and the space-based missions.
This wealth and growth of data rates, volumes, and complexity demanded
applications of automated data processing and analysis tools. While VO and the
individual archives provide data access and some tools, most of the remaining

*
California Institute of Technology, Pasadena, CA 91125, USA
†
Heidelberg Institute for Theoretical Studies, 69118 Heidelberg, Germany
‡
University of California, Irvine, CA 92697, USA
1
astronomical cyberinfrastructure and data analytics tools have been developed by
the individual research groups, captured under the Astroinformatics umbrella.
Today, applications of Machine Learning (ML) and other AI methods are
becoming commonplace and growing rapidly. During the 2021, according to the
Astrophysics Data System (ADS; https://ui.adsabs.harvard.edu), there were about
1000 astronomy/astrophysics papers that involved ML or AI, and their numbers
are growing exponentially, with a doubling time of about 20 months. AI is now a
standard part of the astronomical toolkit.
ML/AI methods are used to create value-added higher level data products for
follow-up research, and may include source detection and segmentation tasks,
structural and morphological classification, as well as all kinds of ordinary
classification and regression tasks. While supervised classification tools are by
construction unable to detect any new types of objects that are not present in the
training data sets, unsupervised clustering offers a possibility of discovering
previously unknown classes, and enable detection of rare, unusual, or even
previously unknown types of objects as outliers in some feature space.
Given the vast scope of the field, the goal of this chapter is not to provide a
comprehensive review, but rather to give some illustrative examples where ML/AI
have enabled significant advances in astronomy.
A useful didactic overview is by [4]. The monograph [5] gives an extensive
and practical coverage of the subject. For some recent examples, see [6].

1.2 Early Applications: Digital Sky Surveys

While there have been some early experiments in the early 1990s, the use of ML/AI
in astronomy really started growing in mid-1990s, with the advent of the first large
digital sky surveys [7,8]. The initial applications were to automate repetitive tasks
that were previously done by humans. A good example of the star-galaxy
separation for the catalogs of objects detected in sky surveys. Following the image
segmentation that identifies individual sources, several tens to hundreds
morphological and structural parameters are evaluated for each one, thus forming
feature vectors that can be analyzed using ML tools. Essentially, first Terabytes
and now Petabytes of images are converted into database catalogs of many millions
to billions of feature vectors, each representing an individual detected source, in
data spaces of hundreds of dimensions, or even thousands once multiple catalogs
are combined.
In the visible, UV, and IR wavelength regimes, the first order classification is
between the unresolved sources (“stars”) and resolved ones (“galaxies”), based
purely on the image morphology. Supervised classification methods, such as the
Artificial Neural Networks (ANN), or Decision Trees (DT) were used effectively
for this task; see, e.g., [9,10]. Morphological classification can be used to identify

2
and remove a variety of instrumental artifacts, that may appear as outliers in the
feature space, [11]. The physical classification as objects of different types, e.g.,
Galactic stars vs. quasars, different types of galaxies, different types of stars, etc.,
requires additional data in a subsequent analysis.
Digital sky surveys opened a new, highly effective mode of astronomical
discovery. Traditional mode of pointed observations focuses on the individual
objects or small samples of objects. Sky surveys may detect billions of sources,
and ML can be used to select and prioritize the most interesting targets for the
follow-up with large and/or space-based telescopes, thus optimizing the use of
these scarce resources. Applying supervised classifiers or cuts in the feature space
informed by the domain expertise has been proved to be very effective in finding
well-defined samples of relatively rare types of objects, such as high-redshift
quasars or brown dwarfs [12,13,14].

1.3 Increasing Challenges: Time-Domain Astronomy

Improvements in the size, quality, and cost of astronomical detectors enabled much
larger format imaging cameras, which in turn enabled the rise of the synoptic sky
surveys, where large areas of sky are surveyed repeatedly. This opening of the
Time Domain enabled systematic, scaled-up studies of various temporal
phenomena, including variability of stars and active galactic nuclei, cosmic
explosions of all kinds (e.g., many types of Supernovae, Gravitational Wave
events, etc.), moving objects such as the potentially hazardous asteroids, etc. Time
Domain – essentially a panoramic cosmic cinematography – touches all fields of
astronomy, from the Solar System to cosmology.
This opens new scientific opportunities, but also brings new challenges in
addition to those posed by the traditional sky surveys, by adding the variability
information to the classification tasks, and often time-criticality due to the
transitive nature of the observed events: the potentially most interesting ones have
to be identified in real time, as they must be followed up before they fade away
[14,15,16,17,18,19,63,64]. Figure 1 shows a conceptual illustration of some of
these challenges.
In addition to the full electromagnetic (EM) spectrum, gravitational wave,
high energy cosmic rays, and neutrino observatories are also now providing
copious amounts of data, opening the field of Multi-messenger Astronomy. In
general, the events detected by these non-EM channels have a very poor
angular resolution and directionality but identifying their EM counterparts is
essential for their physical interpretation. This leads to large area searches for
counterparts, with many potential candidates. ML methods can be used to
classify the possible candidate counterparts, e.g., [20,63,65,66], a n d o ther
ML methods are being used to scrutinize and classify the non-EM signals
themselves, e.g., [21,22].

3
4
these can also be a source of additional systematic errors.
Figure 1: The five major challenges facing TDA today (a) a representation of a data cube signifying multiple wavelengths and
multiwavelength observation of the Crab Nebula, (b) multiplicity of data features, (c) GPRs as a way to bridgegaps in observing,
(d) Understanding effect of noise on objects (from Caldeira & Nord 2020), and (e) detecting anomalies (from Martínez-Galarza
et al. 2021). Image credits: João Steiner, Stephen Todd, ROE and Douglas Pierce-Price, JAC for datacube; NRAO/AUI and M.
Bietenholz; NRAO/AUI and J.M. Uson, T.J. Cornwell (radio); NASA/JPL-Caltech/R. Gehrz / University of Minnesota
(infrared); NASA, ESA, J. Hester and A. Loll / Arizona State University (visible); NASA/Swift/E. Hoversten, PSU (ultraviolet);
NASA/CXC/SAO/F. Seward et al.(X-rays); NASA/DOE/Fermi LAT/R. Buehler (gamma rays) for Crab Nebula images.

process, a variety of interpolation schemes can be employed. However,

events. In the absence of a good theoretical model for the underlying
all quantities at all timestamps are not available. In astronomy, this can
problem, particularly with multidimensional time series where values for

pertain to prioritizing follow-up observations for interesting transient

Predicting the value of a time series between measurements is a common
 One critical issue in classification in general is the poor scaling of the
classification algorithms with the dimensionality of the feature space. This is
especially important in the Time Domain; some approaches have been discussed
by [23,24]. Feature dimensionality from several tens to few hundreds are
now routine. Not all of these are independent (orthogonal) and some even
add to noise for specific classes, making dimensionality reduction a critical
need. For multiclass classification, disambiguating features that are
important for one class but not another can be non-trivial. An example is
the use of binary classifiers for the Zwicky Transient Facility (ZTF) [25].
Tools like DNN and XGBoost can be also used to identify the top features.
When external features (e.g., from crossmatches to other surveys) are being
incorporated, there can be missing features, which further complicates the
use of some of the ML techniques. Techniques like Data Sheets [26] and
Model Cards [27] can be used to standardize data set creation and lead to
reusable models [28].
An alternative is to adopt a probabilistic approach and regard the
observed time series as a single draw from a multivariate Gaussian
distribution fully characterized by a mean (normally assumed to be zero or
constant) and a covariance function. Predicted points then just represent a
subsequent draw and can be calculated with an associated uncertainty.
Gaussian process regression (GPR) [31] uses the observed data to learn the
hyperparameters of the underlying covariance kernel (and mean function if
present). The form of the kernel function is a choice for the user but specific
properties of the underlying process, such as stationarity, autoregressive
behavior, or a spectral density representation, are easily represented. In fact,
there is a theoretical duality between certain GPR kernels and neural
network architectures [32] and neural networks can also be employed
directly as kernels in some GPR implementations.
The main issue in using GPR, particularly with large multidimensional
data sets with thousands of data points and/or comprising thousands of
samples, is the speed of fitting since this typically involves extensive matrix
inversion. Certain GPR implementations have achieved good performance
by making very specific decisions on the functional form of the kernel
function, e.g., it only uses exponential terms, and optimizing accordingly,
but this is not a global solution [33].
It is also unclear how good GPR is at forecasting data. There is a
tendency with non-periodic kernels to regress to the mean with increasing
time past the last observed data point and increasing uncertainty. Recurrent
neural networks seem to show better performance [34], but they have also
been used more in forecasting a next data point rather data over an extended
period of time. Obviously, if the underlying process is nonlinear, then
forecasting presents a much bigger problem and more advanced deep
learning architectures may be required.
Incorporating error-bars in ML analysis is a notoriously non-trivial
challenge. That fact, combined with classifying objects near the detection
5
limit, raises a very different kind of a challenge. Observing ever-fainter
objects helps push the science into newer areas, but at the same time it
comes with a greater risk of such objects turning out to be false positives
(e.g., short lived transients that are below the quiescent limit that brighten
into observable range for a short duration). Uncertainty quantification, e.g.,
[35], combined with emulators and simulators [29], along with models
based on Bayesian techniques may be needed [36].
Looking for anomalies, i.e., objects or events that do not seem to belong
to any of the known classes, poses additional challenges. It is difficult to
define what an anomaly is in the first place: is it an out-of-distribution
object, a completely independent or new class? Will more observations
favor one interpretation or the other, and what kind of observations will be
required? Active learning where newer observations are iteratively used to
improve classification routinely indicate the requirement to revise
classifications at the boundaries of ambiguity. However, the follow-up
resources are limited, and with the ever-growing data rates it becomes
critical to optimize their use. Some early efforts in this arena include
[30,37,38,39,40], and others.

1.4 A Growing Applications Landscape

While classification and outlier search remail a staple of survey-based astronomy,
there is now a much broader range of ML/AI applications.
One application area of ML tools is the estimation of photometric redshifts
(photo-z’s). In cosmology, redshift, reflecting the increase in the scale of the
universe since the light was emitted by some distant object, due to the cosmic
expansion is a measure of distance, and thus necessary in determining the physical
parameters of distant galaxies and quasars, such as their luminosities, masses, etc.
Traditionally, redshifts are measured spectroscopically, which is observationally
expensive. Photo-z’s are a way of estimating the redshifts from the multi-color
photometry, which is observationally much cheaper, and thus can be done for
vastly larger numbers of objects. This is a use case where ML has enabled
significant advances and savings of observing time, by including instrumental
characteristics and physical models implicitly expressed through the data. There
is an extensive literature on this subject with a wide variety of ML methods
[41,42,43,44,45,46,47,48,49,50], and many others). One important conceptual
change was to replace a single number representation of an estimated photo-z with
a probability density distribution.
ML has been also used as a method for the discovery of gravitational lenses,
operating both on the images from sky surveys [51], and time series of quasar
variability [52]. Such large, systematically selected samples of gravitational lenses
can be used as probes of dark matter and the expansion rate of the universe.

6
 In addition to the data obtained through observations, the output of large
numerical simulations is another large source of data calling for an automated
analysis. Current developments led to hybrid approaches of classically computing
physical models in combination with ML models. By doing so, time-consuming
calculations can be replaced through very quick ML models that act as a surrogate
with a similar accuracy as the original code. Thereby, larger volumes, with higher
spatial and temporal resolution, can be computed without requiring more resources.
Another aspect is that critical branching conditions can be detected, and the
resolutions of the simulation can be adaptively changed, ensuring that those details
are not lost or overseen while simulating. Some examples include [53,54,55,56],
and others.
This is just a small sampling of the examples of the diverse, growing, and
creative uses of AI/ML in astronomy.

1.5 Concluding Comments and Future Prospects

While the range and diversity of AI applications in astronomy continue to grow,
most applications so far have been focused on the analysis of already acquired data
sets and their derived data products, such as the tables of pre-extracted and expert
engineered features. However, the landscape of ML/AI applications is also
changing rapidly, affecting different stages of a data-centric approach, data
acquisition, processing, and analysis.
The acquisition stage covers the process of planning and performing
observations. For the most part this process was done by the individual experts,
but based on specified quality criteria, AI systems can learn to perform this
planning automatically. Based on the quick analysis of the initial data, instrument
setup, exposure times, etc., can be used to close the loop between choosing the
right observational setup and getting high quality science data. This kind of fast,
AI-based observation planning and control systems will likely replace the current
way of planning, scheduling, and observing, leading to an improved scientific
outcome, both in quality and quantity of the observations. This will be critical in
the arena of Time-Domain and Multi-Messenger Astronomy, where transient
events may be detected and followed up by a number of different surveys and
facilities, and their prioritization for the follow-up would be essential.
Incorporation of domain knowledge into ML/AI analysis, such as the ‘physics-
based’ AI is an active area of research, with many outstanding challenges
remaining. Some examples include [57,58], and others.
Besides the analysis of scientific data, ML methods get utilized to access
complex scientific content like scientific publications or to realize a natural
language and chat-based access to data stored in catalogs. ML and AI based
systems may transform the way of finding and accessing data soon. Likewise, ML
can be used to sort through the literature given a set of user preferences; an example
is http://www.arxiv-sanity.com/.
7
 Another novel direction is in using AI not just to map the data spaces and find
interesting objects, but to discover potentially interesting relationships that may be
present in the data. One approach is to use symbolic regression, e.g., [59,60]. A
related technique uses memetic regression [61,62].
As the data complexity continues to increase, use of AI to detect interesting
patterns or behaviors present in the data, that may elude humans, e.g., due to the
hyper-dimensionality of the data will keep on increasing. The interpretation of
such AI-based discoveries still rests with the humans, but there is a possibility that
some of them may simply exceed the human cognitive capabilities. We may
increasingly see more examples of a collaborative human-AI discovery.

References

[1] Djorgovski, S. G., Mahabal, A. A., Drake, A., Graham, M. J., and Donalek, C. (2012).
Sky Surveys, in: Astronomical Techniques, Software, and Data, ed. H. Bond, Planets,
Stars, and Stellar Systems, 2, ser. ed. T. Oswalt, (Dordrecht: Springer), pp. 223-281.
[2] Brunner, R. J., Djorgovski, S. G., and Szalay, A. S. (2001). Virtual Observatories of
the Future, A.S.P. Conf. Ser. 225 (San Francisco: Astronomical Society of the
Pacific).
[3] Djorgovski, S. G., and the NVO Science Definition Team (2002). Towards the
National Virtual Observatory, https://www.nsf.gov/mps/ast/sdt_final.pdf
(Washington, DC: National Science Foundation).
[4] Baron, D. (2019). Machine Learning in Astronomy: A Practical Overview, available
online at https://arxiv.org/abs/1904.07248
[5] Ivezić, Ž., Connolly, A., VanderPlas, J., and Gray, A. (2020). Statistics, Data
Mining, and Machine Learning in Astronomy: A Practical Python Guide for the
Analysis of Survey Data. (Princeton: Princeton University Press).
[6] Zelinka, I., Brescia, M., and Baron, D. (editors) (2021). Intelligent Astrophysics, In:
Emergence, Complexity and Computation, 39, Springer Nature.
[7] Weir, N., Fayyad, U., Djorgovski, S. G., and Roden, J. (1995a). The SKICAT System
for Processing and Analysing Digital Imaging Sky Surveys, Publ. Astron. Soc.
Pacific 107, 1243-1254.
[8] Fayyad, U., Smyth, P., Weir, N., and Djorgovski, S. G. (1995). Automated Analysis
and Exploration of Image Databases: Results, Progress, and Challenges, J. Intel.
Inform. Sys. 4, 7.
[9] Weir, N., Fayyad, U., and Djorgovski, S. G. (1995b). Automated Star/Galaxy
Classification for Digitized POSS-II, Astron. J. 109, 2401-2414.
[10] Odewahn, S., de Carvalho, R., Gal, R., Djorgovski, S. G., Brunner, R., Mahabal, A.,
Lopes, P., Kohl Moreira, J., & Stalder, B. (2004). The Digitized Second Palomar

8
 Observatory Sky Survey (DPOSS). III. Star-Galaxy Separation, Astron. J. 128, pp.
3092-3107.
[11] Donalek, C., Mahabal, A., Djorgovski, S. G., Marney, S., Drake, A., Graham, M.,
Glikman, E., and Williams, R. (2008). New Approaches to Object Classification in
Synoptic Sky Surveys, AIP Conf. Ser., 1082, pp. 252-256.
[12] Djorgovski, S. G., Mahabal, A., Brunner, R., Gal, R., Castro, S., de Carvalho, R., and
Odewahn, S. (2001a). Searches for Rare and New Types of Objects, in: Virtual
Observatories of the Future, eds. R. Brunner, S.G. Djorgovski, and A. Szalay, A.S.P.
Conf. Ser. 225, pp. 52-63.
[13] Djorgovski, S. G., Brunner, R., Mahabal, A., Odewahn, S., de Carvalho, R., Gal, R.,
Stolorz, P., Granat, R., Curkendall, D., Jacob, J., and Castro, S. (2001b). Exploration
of Large Digital Sky Surveys, in: Mining the Sky, eds. A. J. Banday et al., ESO
Astrophysics Symposia, (Berlin: Springer), pp. 305-322.
[14] Djorgovski, S.G., Mahabal, A., Brunner, R., Williams, R., Granat, R., Curkendall,
D., Jacob, J., and Stolorz, P. (2001c). Exploration of Parameter Spaces in a Virtual
Observatory, in: Astronomical Data Analysis, eds. J.-L. Starck & F. Murtagh, Proc.
SPIE 4477, pp. 43-52.
[15] Mahabal, A., Djorgovski, S. G., Drake, A., Donalek, C., Graham, M., Moghaddam,
B., Turmon, M., Williams, R., Beshore, E., and Larson, S. (2011). Discovery,
Classification, and Scientific Exploration of Transient Events from the Catalina Real-
Time Transient Survey, Bull. Astr. Soc. India, 39, 387-408.
[16] Djorgovski, S. G., Mahabal, A., Drake, A., Graham, M., Donalek, C., & Williams,
R., (2012a). Exploring the Time Domain with Synoptic Sky Surveys, in: Proc. IAU
Symp. 285: New Horizons in Time Domain Astronomy, eds. E. Griffin et al.,
(Cambridge: Cambridge Univ. Press), pp. 141-146.
[17] Djorgovski, S. G., Mahabal, A., Donalek, C., Graham, M., Drake, A., Moghaddam,
B., and Turmon, M. (2012b). Flashes in a Star Stream: Automated Classification of
Astronomical Transient Events, Proc. IEEE e-Science 2012, (IEEE press), 6404437.
[18] Graham, M., Djorgovski, S. G., Mahabal, A., Donalek, C., Drake, A., and Longo, G.
(2012). Data Challenges of Time Domain Astronomy, Distributed and Parallel
Databases, 30, pp. 371-384.
[19] Graham, M., Drake, A., Djorgovski, S. G., Mahabal, A., and Donalek, C. (2017).
Challenges in the automated classification of variable stars in large databases, in:
Wide-Field Variability Surveys: A 21st Century Perspective, eds. Catelan, M. and
Gieren, W., EPJ Web of Conferences, 152, 03001.
[20] Andreoni, I., Coughlin, M., Kool, E., Kasliwal, M., Kumar, H., Bhalerao, V.,
Carracedo, A., Ho, A., Pang, P., Saraogi, D., et al. Astrophys. J. 918, 63 (2021).
[21] Cabero, M., Mahabal, A., and McIver, J., Astrophys. J. Lett. 904, L9 (2020).
doi:10.3847/2041-8213/abc5b5 [arXiv:2010.11829 [gr-qc]].
[22] Abbott, T.C., Buffaz, E., Vieira, N., Cabero, M., Haggard, D., Mahabal, A. and
McIver, J., Accepted to Astrophys. J., 2022. GWSkyNet-Multi: A Machine Learning
Multi-Class Classifier for LIGO-Virgo Public Alerts.
https://arxiv.org/abs/2111.04015.

9
[23] Donalek, C., Kumar, A., Djorgovski, S.G., Mahabal, A., Graham, M., Fuchs, T.,
Turmon, M., Sajeeth Philip, N., Yang, T.-C., and Longo, G. (2013). Feature Selection
Strategies for Classifying High Dimensional Astronomical Data Sets, in: Scalable
Machine Learning: Theory and Applications, IEEE BigData 2013, 35-40.
[24] D'Isanto, A., Cavuoti, S., Brescia, M., Donalek, C., Longo, G., Riccio, G.,
Djorgovski, S. G. (2016). An Analysis of Feature Relevance in the Classification of
Astronomical Transients with Machine Learning Methods, MNRAS 457, pp. 3119-
3132.
[25] van Roestel J., Duev D. A., Mahabal A. A., Coughlin M. W., Mr´oz P., Burdge K.,
Drake A., et al. (2021). Astron. J, 161, 267.
[26] Gebru T., Morgenstern J., Vecchione B., Wortman Vaughan J., Wallach H., Daumé
H., Crawford, K. (2018). Online at https://arxiv.org/abs/1803.
[27] Mitchell M., Wu S., Zaldivar A., Barnes P., Vasserman, L., Hutchinson B., Spitzer
E., et al., 2019, FAT* '19: Conference on Fairness, Accountability, and
Transparency, https://arxiv.org/abs/1810.03993.
[28] Mahabal, A., Hare, T., Fox, V., Hallinan, and G. (2021). In-space Data Fusion for
More Productive Missions. Bull. AAS, 53 (4).
[29] Caldeira, J. and Nord, B., 2020. Deeply uncertain: comparing methods of uncertainty
quantification in deep learning algorithms. Machine Learning: Science and
Technology, 2(1), 015002.
[30] Martínez-Galarza J. R., Bianco F. B., Crake D., Tirumala K., Mahabal A. A., Graham
M. J., Giles D., 2021, MNRAS, 508, 5734.
[31] Rasmussen, C., and Williams, C., Gaussian Processes for Machine Learning (2006).
MIT Press.
[32] Lee, J., Bahri, Y., Novak, R., Schoenholz, S., Pennington, J., Sohl-Dickstein, (2017)
Deep neural networks as gaussian processes https://arxiv.org/abs/1711.00165.
[33] Foreman-Mackey, D., Agol, E., Ambikasaran, S., and Angus, R. (2017). Fast and
scalable Gaussian process modeling with applications to astronomical time series,
Astron. J., 154, 220.
[34] Tachibana, Y., Graham, M., Kawai, N., Djorgovski, S. G., Drake, A., and Mahabal,
A. (2020). Deep Modeling of Quasar Variability, Astrophys. J., 903, 17.
[35] Abdar, M., Pourpanah, F., Hussain, S., Rezazadegan, D., Liu, L., Ghavamzadeh, M.,
Fieguth, P., Cao, X., Khosravi, A., Acharya, U.R. and Makarenkov, V. A review of
uncertainty quantification in deep learning: Techniques, applications and
challenges. Information Fusion, 76, 243-297 (2021).
[36] Walmsley M., Smith L., Lintott C., Gal Y., Bamford S., Dickinson H., Fortson L., et
al. (2020). Galaxy Zoo: probabilistic morphology through Bayesian CNNs and
active learning, MNRAS, 491, 1554-1574.
[37] Webb S., Lochner M., Muthukrishna, D., Cooke J., Flynn, C., Mahabal A., Goode
S., et al., 2020, MNRAS, 498, 3077.

10
[38] Villar, V. A., Cranmer, M., Berger, E., Contardo, G., Ho, S., Hosseinzadeh, G., Lin,
J. (2021). A Deep-learning Approach for Live Anomaly Detection of Extragalactic
Transients, Astrophys. J. Suppl. Ser., 255, 24.
[39] Ishida E. E. O., Kornilov M. V., Malanchev K. L., Pruzhinskaya M. V., Volnova A.
A., Korolev V. S., Mondon F., et al., 2021, Astron, Astrophys., 650, A195.
[40] Lochner, M., and Bassett, B. (2021). ASTRONOMALY: Personalised active
anomaly detection in astronomical data, Astron. Computing, 36, 100481.
[41] Ball, N., Brunner, R., Myers, A., Strand, N., Alberts, S., and Tcheng, D. (2008).
Robust Machine Learning Applied to Astronomical Data Sets. III. Probabilistic
Photometric Redshifts for Galaxies and Quasars, Astrophys. J., 683, 12-21.
[42] Laurino, O., D'Abrusco, R., Longo, G., and Riccio, G. (2011). Astroinformatics of
galaxies and quasars: a new general method for photometric redshifts estimation,
MNRAS 418, 2165-2195.
[43] Brescia, M., Cavuoti, S., D'Abrusco, R., Longo, G., and Mercurio, A. (2013).
Photometric Redshifts for Quasars in Multi-band Surveys, Astrophys. J., 772, 140.
[44] Carrasco Kind, M., and Brunner, R. (2014). Exhausting the information: novel
Bayesian combination of photometric redshift PDFs, MNRAS, 442, 3380-3399.
[45] Cavuoti, S., Brescia, M., Longo, G., and Mercurio, A. (2012). Photometric redshifts
with the quasi-Newton algorithm (MLPQNA): Results in the PHAT1 contest, Astron.
Astrophys., 546, A13.
[46] Cavuoti, S., Amaro, V., Brescia, M., Vellucci, C., Tortora, C., and Longo, G. (2017).
METAPHOR: A machine-learning-based method for the probability density
estimation of photometric redshifts, MNRAS, 465, 1959-1973.
[47] D'Isanto, A., and Polsterer, K. (2018). Photometric redshift estimation via deep
learning. Generalized and pre-classification-less, image based, fully probabilistic
redshifts, Astron. Astrophys., 609, A111
[48] Salvato, M., Ilbert, O., and Hoyle, B. (2019). The many flavours of photometric
redshifts, Nature Astronomy, 3, 212-222.
[49] Schmidt, S.J., et al., LSST Dark Energy Science Collaboration (2020). Evaluation
of probabilistic photometric redshift estimation approaches for The Rubin
Observatory Legacy Survey of Space and Time (LSST), MNRAS 499, 1587-1606.
[50] Razim, O., Cavuoti, S., Brescia, M., Riccio, G., Salvato, M., and Longo, G. (2021).
Improving the reliability of photometric redshift with machine learning, MNRAS,
507, 5034-5052.
[51] Krone-Martins, A., Delchambre, L., Wertz, O., Ducourant, C., Mignard, F., Teixeira,
R., et al. (2018). Gaia GraL: Gaia DR2 gravitational lens systems. I. New quadruply
imaged quasar candidates around known quasars, Astron. Astrophys., 616, L11.
[52] Krone-Martins, A., Graham, M., Stern, D., Djorgovski, S. G., Delchambre, L.,
Ducourant, C., et al. (2022). Gaia GraL: Gaia DR2 Gravitational Lens
Systems.V.Doubly-imaged QSOs Discovered from Entropy and Wavelets, Astron.
Astrophys. in press.

11
[53] Kamdar, H., Turk, M., and Brunner, R. (2016). Machine learning and cosmological
simulations - II. Hydrodynamical simulations, MNRAS, 457, 1162-1179.
[54] Ni, Y., Li, Y., Lachance, P., Croft, R., Di Matteo, T., Bird, S., and Feng, Y. (2021).
AI-assisted superresolution cosmological simulations - II. Halo substructures,
velocities, and higher order statistics, MNRAS, 507, 1021-1033.
[55] Lovell, C., Wilkins, S., Thomas, P., Schaller, M., Baugh, C., Fabbian, G., Bahé, Y.
(2022). A machine learning approach to mapping baryons on to dark matter haloes
using the EAGLE and C-EAGLE simulations, MNRAS, 509, 5046-5061.
[56] Chacón, J., Vázquez, J., and Almaraz, E. (2022). Classification algorithms applied
to structure formation simulations, Astron. Computing, 38, 100527.
[57] Karniadakis, G., Kevrekidis, I., Lu, L., Perdikaris, P., Wang, S., and Yang, L. (2021).
Physics-informed machine learning, Nature Reviews Physics, 3(6):422–440.
[58] Liu, Z., Chen, Y., Du, Y., and Tegmark, M. (2021). Physics-Augmented Learning:
A New Paradigm Beyond Physics-Informed Learning,
https://arxiv.org/abs/2109.13901
[59] Graham, M., Djorgovski, S. G., Mahabal, A., Donalek, C., and Drake, A. (2013).
Machine-Assisted Discovery of Relationships in Astronomy, MNRAS, 431, 2371.
[60] Udrescu, S.-M., and Tegmark, M. (2020). AI Feynman: a Physics-Inspired Method
for Symbolic Regression, Science Advances, 6:2631.
[61] Sun, H., and Moscato, P. (2019). A Memetic Algorithm for Symbolic Regression,
in: 2019 IEEE Congress on Evolutionary Computation (CEC), 2167-2174.
[62] Moscato, P., Sun, H., and Haque, M. (2021). Analytic Continued Fractions for
Regression: A Memetic Algorithm Approach, Expert Systems with Applications,
179, 115018.
[63] Djorgovski, S. G., Graham, M., Donalek, C., Mahabal, A., Drake, A., Turmon, M.,
and Fuchs, T. (2016). Real-Time Data Mining of Massive Data Streams from
Synoptic Sky Surveys, Future Gen. Comp. Sys., 59, 95-104.
[64] Djorgovski, S. G., Mahabal, A., Donalek, C., Graham, M., Drake, A., Turmon, M.,
Fuchs, T. (2014). Automated Real-Time Classification and Decision Making in
Massive Data Streams from Synoptic Sky Surveys, Proc. IEEE e-Science 2014, ed.
C. Medeiros, (IEEE press), pp. 204-211.
[65] Mahabal, A., Sheth, K., Gieseke, F., Pai, A., Djorgovski, S.G., Drake, A., Graham,
M., and CSS/CRTS/PTF Teams (2017). Deep-Learnt Classification of Light Curves,
in 2017 IEEE Symp. on Computational Intelligence (SSCI), 2757-2764.
[66] Mahabal, A., et al. (ZTF Team) (2019). Machine Learning for the Zwicky Transient
Facility, Publ. Astron. Soc. Pacific 131, 038002.

12