PoS(APCS2018)051 https://pos.sissa.it/ ∗† [email protected] [email protected] [email protected] emille.ishida@[email protected] [email protected] [email protected] [email protected] Copyright owned by the author(s) under the terms of the Creative Commons c Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). Vladimir Korolev Central Aerohydrodynamic Institute, 1 Zhukovsky st,Russia Zhukovsky, Moscow Region, 140180, Moscow Institute of Physics and Technology141701, , Russia 9 Institutskiy per., Dolgoprudny, MoscowE-mail: Region, Alina Volnova Space Research Institute of the RussianMoscow, Academy Russia, of 117997 Sciences (IKI), 84/32E-mail: Profsoyuznaya Str, Emille E.O. Ishida Université Clermont Auvergne, CNRS/IN2P3, LPC, F-63000E-mail: Clermont-Ferrand, France Florian Mondon Université Clermont Auvergne, CNRS/IN2P3, LPC, F-63000E-mail: Clermont-Ferrand, France Matwey Kornilov Lomonosov Moscow State University, Sternberg AstronomicalMoscow Institute, 119234, Universitetsky pr. Russia 13, National Research University Higher School ofMoscow Economics 105066, 21/4 Russia Staraya Basmannaya Ulitsa, E-mail: Maria Pruzhinskaya Lomonosov Moscow State University, Sternberg AstronomicalMoscow Institute, 119234, Universitetsky pr. Russia 13, E-mail: Konstantin Malanchev Lomonosov Moscow State University, Sternberg AstronomicalMoscow Institute, 119234, Universitetsky pr. Russia 13, National Research University Higher School ofMoscow Economics, 105066, 21/4 Russia Staraya Basmannaya Ulitsa, E-mail: Machine Learning Analysis of Supernova Light Curves PoS(APCS2018)051 ) http://sne.space/ Speaker. https://pruzhinskaya.com/snad/ The next generation of astronomical surveys will revolutionizeraising our unprecedented understanding data of the challenges Universe, in thehuman process. scanning One for of them the is identificationgiven the of that impossibility most to unusual/unpredicted of rely astrophysical on the objects. availableacterization data cannot Moreover, will rely be on in the existence the ofduce form an high of analysis resolution photometric of spectroscopic anomaly observations, observations. detection such We in intro- char- the Open Supernova Catalog ( with use of machine learning. Weare developed a identified strategy and and then pipeline submitted — to wheretive careful strategy anomalous to individual objects guarantee analysis. we This shall not projectso overlook represents exciting hard an new to science effec- acquire. hidden in the data we fought † ∗ Accretion Processes in Cosmic Sources —3–8 II September - 2018 APCS2018 Saint Petersburg, Russian Federation PoS(APCS2018)051 ] ] 18 19 ] tasks. 16 30 similar , ∼ 15 ], in particular 2 Maria Pruzhinskaya ] and subspace analysis [ ] and regression [ 17 14 , 13 , 12 , 11 , 10 , 1 9 Ni, ASASSN-15lh — for some time it was considered 56 ], where scientific questions drive the development of new 8 ]. Although all of this has been done to periodic variables there 20 ], but the synergy is far from that achieved by other endeavors in 5 , 4 , ] or medicine [ 3 7 ]), SN 2005bf — supernova attributed to SN Ib but with two broad maxima on 1 ], ecology [ 6 ]. We use the Isolation Forest as an outlier detection algorithm that identifies anomalies 21 [ https://sne.space/ In this study we search the anomalies in photometrical data of the Open Supernova Cata- Astronomers have already benefited from developments in machine learning [ Astronomical anomaly detection has not been yet fully implemented in the enormous amount Supernova stars (SNe) are ones of the most beautiful and interesting objects in the Universe. The generation of precise, large, and complete supernova surveys in the last years has increased The lack of spectroscopic support makes the photometrical supernova typing top required. The 1 1 log for exoplanet search [ methods. More recently, random forest algorithmsor in have been hybrid extensively statistical used analysis by [ is themselves not [ much done for transients and even less for supernova. genetics [ of data that has been gathered.studies can As a be matter divided of into fact, only barring two a few different exceptions, trends: most of clustering the [ previous LCs, SN 2010mb — unusualis SN not Ic consistent with with very radioactive decay lowas of decline the rate most after luminous the supernova ever maximum observedthe brightness (two origin that times of brighter than this super-luminous object SNe),sequence later was star challenged by and a black nowof hole. it the is Finding main such considered aims objects of as the (and acan current then be tidal project. studying framed disruption As them as such of more an sources a anomaly closely) are detection main- is typically problem. one rare, the task of finding them algorithms. Moreover, given the relatively recentin advent astronomy of are large concentrated data in classification sets, [ most of the ML efforts They are responsible for chemicaltheir enrichment energetic of explosions interstellar causes medium; themoreover, thanks star density to formation; SNe waves we induced SNe are by are studyingdefines the origin its composition following of and destiny. distance high scale energy of the cosmic Universe rays; which the need of developing automatedentific analysis observations tools present to both process greatlearning this opportunities (ML) large and researchers. amount challenges of for data. astronomers and These machine sci- analysis of big supernova dataset with MLon methods base is of needed N-parameter to distinguish grid. thesupernova Such supernova contamination by study as types allows well — us the to problem,that purify which collect the is SN considered relevant candidates for SN all without sample large carefulindicators from supernova analysis database (proximity non- of to each the candidate galaxies, andabsolute basing transient magnitude). on behavior, It the arise/decline is secondary also rateSNe expected on that with light during unusual curves such properties (LCs), analysis can theSN unknown be 2006jc variable detected. — objects SN or As with an very example strong of but unique relatively narrow objects He one I can lines refer in to early spectra ( Machine Learning Analysis of Supernova Light Curves 1. Introduction objects are known, [ PoS(APCS2018)051 4 3 of 10 = 3 > × 10 ). After × 5 2.3 of SNe LCs ∼ 3 10 , and 404 objects × Maria Pruzhinskaya filters. We assume ). We require gri 4 ∼ 2.2 BRI or gri , 0 i filters using the Lupton’s (2005) 0 (see Sect. ]. The catalog is constructed by r 0 , 767 objects in g 0 21 gri i gri 0 r 0 to g into BRI BRI 10 photometrical observations and 2 > gri and transform gri and ]. This technique is based on the fact that anomalies are data of SNe have 4 22 BRI 10 × 2 . These equations are derived by matching SDSS DR4 photometry to . 2 1 ∼ filters are close enough to 0 i 0 600 SNe with spectra. ). r 0 To increase the sample we convert the Bessel’s http://www.sdss3.org/dr8/algorithms/sdssUBVRITransform.php The catalog contains the data in different photometrical passbands. To have a more homoge- Our choice is justified by the fact that the catalog incorporates the data for more than 5 The data are drawn from the Open Supernova Catalog [ g ∼ 2 BRI transformation equations Peter Stetson’s published photometry for stars: neous data sample, we chose only those SNe that have LCs in 2.2 Transformation between and in combining many publicly available data sourcespernova (such as Project, Asiago Gaia Supernova Photometric Catalog, Science CarnegieTelescope Su- Alerts, & Nearby Rapid Supernova Response Factory, System Panoramicnomical (Pan-STARRS), Survey SDSS Institute Supernova Supernova Light Survey, Curve Sternberg Catalogue, Supernova Astro- LegacyAll-Sky Survey Automated (SNLS), MASTER, Survey for Supernovaetions. (ASAS-SN), iPTF, It etc.) represents an and open repository fromdownloadable for individual format. supernova publica- metadata, This light catalog curves, also and includes spectra in some an contamination easily from non-SN objects. SNe/SNe candidates ( SNe have spectra). For comparison, SDSS supernova catalog contains only that photometrical points in each filter withour a approach aims 3-day to binning. deal This withthe threshold big cadence is data of justified future where by transient the surveys the human doesfor fact expertise not that will all allow not to the get be transients a possible. well-sampled withthreshold However, multicolour a does light nice curve not coverage. mean that ConsideringWe we need the have them a sample to little we better number work reconstruct ofthis with, a cut, points the our "poor" on sample light "3-points" multicolour contains curve 3197 light basing objects curve (2026 on in objects the total. in others (see Sect. 2. Data 2.1 The Open Supernova Catalog Machine Learning Analysis of Supernova Light Curves instead of normal observations [ points that are few and(isolation) different. trees. Similarly to Random Forest it is built on an ensemble of binary PoS(APCS2018)051 (2.1) AUSSIAN i G , the results 56640 ]. Solid lines 1 25 , Maria Pruzhinskaya 24 56590 , 23 ). ULTIVARIATE 56540 2 filters [ 5 1e filters with use of Lupton’s (2005) gri 56490 1.0 0.8 0.6 0.4 0.2 0.0 gri . Obviously, in the Open Supernova 1313 2271 0885 0038 0971 1439 3820 3974 ...... r to 0 0 0 0 0 0 0 0 56640 gri − − − − − BR ) + ) + ) + ) ) ) ) ) i i z r r r g g ) are enough (Fig. − − − − − − − − 56590 i r r g g g u u ( ( ( ( ( ( ( ( MJD BRI 3 3780 2936 2444 56540 3130 5784 1837 . . . 8116 2906 . . . . . 0 0 1 0 0 0 0 0 5 − − − + − − − − i r r 1e r g g u g 56490 = 0.2 0.0 1.0 0.8 0.6 0.4 ======I I with the original ones. As it is seen from the Fig. R R B B V V g 56640                                  gri 56590 56540 5 1e interpolation (RBF kernel). For each object it allows to correlate its multicolour LCs 56490

Light curves of SN2013ej. Points are the observations in 0.4 0.2 0.0 1.0 0.8 0.6 Flux, relative units relative Flux, 3 ). First, we tried to use two Bessel’s filters to get 2.3 https://github.com/matwey/gp-multistate-kernel It is more convenient to implement the ML algorithm to the data with uniform time grid which Before to apply the filter transformation, we fitted the LCs with Gaussian processes (see 3 ROCESS P Catalog more objects have photometry only inis two enough filters than we in will three, and haveonly, if we a such made a larger a transformation sample. test:and we To chose compared check few the the objects transformed with quality LCs of available transformation in both, with SDSS two and filters Bessel’s filters, are the approximation of results of the transformation from Figure 1: 2.3 LCs fit is unfortunately not the casedistributed with data supernovae. onto uniform Commonly grid used iscurve is to technique fitted fit to by them transform GP with independently. unevenly Gaussian However, in processes this (GP). study Usually, we each use light the M transformation equations. and approximates the data by GP in all filters in a one global fit (for details see Kornilov et. 2019, Sect. Machine Learning Analysis of Supernova Light Curves of comparison are unsatisfactory.analysis. This The means same that test at showed least that three one filters more ( filter has to be added in the PoS(APCS2018)051 ], 26 light i , r i 56640 ]. Solid lines 25 , Maria Pruzhinskaya 24 56590 , 23 3 fluxes in three bands, × 56540 ). filters [ 5 3 1e filters with use of Lupton’s (2005) filter and the kernel parameters. gri 56490 0.6 0.4 0.2 0.0 1.0 0.8 r gri was done, we checked the results of r filter is reproduced from the to 56640 g ], for dimensionality reduction of the data BRI 27 ROCESS 56590 P MJD 4 56540 5 AUSSIAN 1e G 56490 0.2 0.0 1.0 0.8 0.6 0.4 g 56640 56590 ULTIVARIATE 56540 5 1e days with 1-day bin relative to the LC maximum in 56490

Light curves of SN2013ej. Points are the observations in 0.6 0.4 0.2 0.0 1.0 0.8

] Flux, relative units relative Flux, 100 , Based on the results of approximation we extracted photometry (in flux) in the range of When the fit by M After the approximation procedure, each object has 373 features: 121 Each object has its own flux scale due to the different origin and different distance. So, before Isolation forest is an ensemble of random isolation trees. Each isolation tree is a space parti- 20 − These values were used as features for our ML algorithm (see Sect. [ approximation by eye. Thoseeration SNe (mainly with the unsatisfactory objects fit with werebigger bad removed temporal photometrical from coverage. quality). In the We the further also end extrapolated consid- we the got fit a to sample have that a consists on 1999 objects. curves. This correlation does not assume any physical assumptions about LC shape. a variation of stochastic neighbor embedding method [ in prep.). With this techniquein we can other reconstruct filters. the missing For parts example, of LC in basing Fig. on LC 4 behaviour the maximum in the dimensionality reduction procedure we normalizedits each maximum value vector and of used 363 the photometrical maximum value points as by one more feature. Then, we applied t-SNE [ tioning tree similar to a widely-know Kd-tree. However, in contrast to Kd-tree, space coordinate (a are approximation of the resultstransformation equations. of the transformation from 3. Anomaly detection 9 fitted parameters of Gaussian Processtwo kernel, cases and of logarithm of outliers likelihooddimensionality search: of reduction. the with fit. all We examine features and with smaller3.1 number of Dimensionality Reduction features obtained by with 374 features. Finally, we obtained 7 feature reduced data sets:3.2 from Methods: 2 Isolation to Forest 8 features. Figure 2: Machine Learning Analysis of Supernova Light Curves PoS(APCS2018)051 ] 21 mag 34 − ] suggests , ] ] < 30 33 30 36 , M ] , ] , 32 28 29 31 35 Maria Pruzhinskaya ) and obtained a list of 3.1 . Ni 56 ). This peculiar supernova has large peak optical 4 5 List of found anomalies. ], see Fig. 29 Table 1: ). SNe Ia-91T are characterized by higher peak luminosity and ] SLSN can be divided into three broad classes: SLSN-I without ]. SNe Ia are used as universal distance ladder since their luminosity 3 100 outliers among a total 1999 objects. Using the publicly available 41 39 , ∼ 38 , 37 ], classified by our code as anomaly, belongs to the so-called 1991T-like- 28 and described below, the rest are still being studied. 1 SN2013cvSN1000+0216 10 00 16SN2006kg 05.87 22 +02 43.16 16 +18 23.6 57 35.6Gaia16aye SLSN SN Ia-pec 01 04 16.98 +00 46 08.9 19 40 01.13 +30 AGN 07 53.4 Binary microlensing event [ [ [ [ SN2016bln 13 34 45.49 +13 51 14.3 SN Ia-91T [ Name Coordinates Object type Ref. Superluminous SNe (SLSN) are supernovae with an absolute peak magnitude SN2016bln [ Another novelty is SN2013cv ( [ Type Ia supernova phenomenon is an explosion of a carbon-oxygen white dwarf that exceed We run the Isolation Forest algorithm on each data set (see Sect. We visually inspected that SN2013cv is an intermediate case between the normal and4.2 super-Chandrasekhar events. Superluminous SNe in any band. Accordinghydrogen to in their [ spectra, hydrogen-rich SLSN-IIstellar that often material show signs (CSM), of and interactionevolving with finally, LCs, circum- powered SLSN-R, by a the radioactive rare decay of class of hydrogen-poor events with slowly at maximum light is approximately theall same. of However, SNe them Ia are can suitable be for divided cosmology. by subtypes and not supernovae subtype (see Fig. broader LCs than "normal" SN Ia, and different early spectrum evolution. and UV luminosity and show an absence of iron absorption lines in the early spectra. [ the Chandrasekhar limit eitheranother by white dwarf matter [ accretion from a companion star or by merging with 4.1 Peculiar SNe Ia feature) and a split value are selectedleads at to random an for every unbalanced node tree ofproperty. the unusable A isolation path for tree. distance This spatial between algorithm search,space the but root from and the "normal" a tree data. leaf hasroot-leaf is This path the shorter distance allows following on for us average important every for data to samplethe points construct that path distanced enough we length. in have, random and trees then rank to the estimate data samples average based on sources we checked what kindlisted of in astrophysical Table objects they are. The most prominent outliers are Machine Learning Analysis of Supernova Light Curves anomalies. 4. Results PoS(APCS2018)051 ). 7 i i 57600 56500 ). The following 6 Maria Pruzhinskaya 57550 56450 7 7 ], see Fig. 57500 1e 1e 32 3.0 2.5 2.0 1.5 1.0 0.5 0.0 1.25 1.00 0.75 0.50 0.25 0.00 ]. Solid lines are the results of our ]). 33 r 34 , , r ]. 57600 9. It may be an example of a pulsational 30 ]. Solid lines are the results of our approxi- . 33 31 3 40 56500 = z . MJD 57550 MJD 6 56450 . ROCESS 7 P 7 57500 1e 1e ROCESS 2 1 0 4 3 1.0 0.5 0.0 2.5 2.0 1.5 P AUSSIAN G g filters of peculiar SN2013cv [ g 57600 filters of SN Ia-91T 2016bln [ ) was discovered in the framework of the Canada-France-Hawaii Tele- AUSSIAN 5 gri 56500 G gri ] is an object with the most non-SN behavior in our set of outliers (Fig. 57550 ULTIVARIATE 35 56450 7 7 ULTIVARIATE Light curves in 1e 57500 Light curves in 1e

0 2 1 4 3 0.0 2.0 1.5 1.0 0.5

Flux, relative units relative Flux, Flux, relative units relative Flux, ] it was reported that Gaia16aye is a binary microlensing event — gravitational microlensing SN 1000+0216 (Fig. SN2006kg was erroneously classified as Type II supernovae ( [ Gaia16aye [ 36 In [ by binary systems — the first ever discovered towards the Galactic Plane. approximation by M 4.3 AGN studies identified it as an active galactic nucleus (AGN, [ 4.4 Binary microlensing event scope Legacy Survey Deep Fields and has a redshift pair-instability SN or a SLSN-IIaction which between extreme the optical expanding emission ejecta is and massive explained CSM by [ the strong inter- Figure 4: Figure 3: mation by M Machine Learning Analysis of Supernova Light Curves PoS(APCS2018)051 i' i' i 57750 54450 54050 Maria Pruzhinskaya 57700 54400 http://gsaweb.ast. 54000 5 8 10 57650 1e 1e 1e 54350 ]. Solid lines are the results of our 2.0 1.5 1.0 0.5 0.0 1.0 0.8 0.6 0.4 0.2 0.0 2.0 1.5 1.0 0.5 0.0 31 r' r r' 57750 54450 ). Solid lines are the results of our approxima- 54050 . MJD 57700 MJD ]. Solid lines are the results of our approximation by MJD 54400 7 34 ROCESS 54000 8 5 P 10 . 57650 1e 1e 1e 54350 0.4 0.2 0.0 0.4 0.2 0.0 1.0 0.8 0.6 0.8 0.6 . ROCESS 1.25 1.00 0.75 0.50 0.25 0.00 AUSSIAN P G g' g' 57750 filters of binary microlensing event Gaia16aye ( 54450 ROCESS filters of SN2006kg [ filters of superluminous SN1000+0216 [ P gri gri AUSSIAN gri 54050 G 57700 ULTIVARIATE 54400 AUSSIAN g G 54000 6 8 11 57650 1e 1e Light curves in Light curves in Light curves in ULTIVARIATE 1e 54350

0 3 2 1 6 5 4 0.5 0.0 1.5 1.0 2.5 2.0 0.0 0.8 0.6 0.4 0.2

Flux, relative units relative Flux, Flux, relative units relative Flux, Flux, relative units relative Flux, ULTIVARIATE M cam.ac.uk/alerts/alert/Gaia16aye/followup tion by M Figure 7: Figure 6: Figure 5: Machine Learning Analysis of Supernova Light Curves approximation by M PoS(APCS2018)051 , Maria Pruzhinskaya International Massive stars , ) filters by Gaussian 100 anomalies, among gri ]) will discover over ten ∼ 42 SNe, but before these SNe will ]. 5 10 ∼ ]. 0906.2173 43 ,[ ]. 8 (Kornilov et al. 2019, in prep.) was specially developed 1509.09069 ,[ (2010) 1049–1106 KERNEL 19 Data Mining and Machine Learning in Astronomy - MULTISTATE - (Feb., 2016) 853–869 machine learning software was used [ GP 456 LEARN - Journal of Modern Physics D exploding in a He-rich circumstellar medium - IX. SN 2014av, and characterization of Type Ibn SNe MNRAS The development of large synoptic sky surveys has led to a discovery of huge number of We used the Isolation Forest algorithm to search the anomalies in the Open Supernova Cata- M. Pruzhinskaya and M. Kornilov are supported by RFBR grant according to the research This research has made use of NASA’s Astrophysics Data System Bibliographic Services. [2] N. M. Ball and R. J. Brunner, [1] A. Pastorello, X.-F. Wang, F. Ciabattari, D. Bersier, P. A. Mazzali, X. Gao et al., SCIKIT References supernovae and supernova candidates. Among thetroscopical SN confirmation. discovered every year, The only amount 10%already of have spec- beyond astronomical human data increases capabilities. dramaticallydates, While with during time now ten-year and community survey has Large Synoptic dozens Sky of Telescope thousands (LSST, SN [ candi- log. During the data pre-processing we fitted the supernova LCs in three ( project 18-32-00426\18 for anomaly analysis and LCsRBFR interpolation. grant K. 18-32-00553 Malanchev is for supported preparingedges by Open support Supernova from CNRS Catalog 2017 data. MOMENTUMoretical grant E. physics and E. Foundation and O. for Mathematics Ishida the18-12-00522 "BASIS". advancement acknowl- for of the- analysis A. of Volnova interpolated acknowledgesMoscow LCs. support State from We University used Program RSF the of grant equipment Development.skaya) funded acknowledge The by the authors the support (K. Lomonosov from MalanchevState the and University M. Program (Leading Pruzhin- Scientific of School development "Physics of of M.V. stars, Lomonosov relativistic Moscow objects and galaxies"). Machine Learning Analysis of Supernova Light Curves 5. Conclusions million supernovae (and only a smallThe fraction of LSST them cadence will will receive allow a tobe spectroscopical receive used confirmation). the in light any curves physical for analysis,tion they must and be to classified extract by all types.approach possible In will knowledge, order allow to machine not process learning only this techniques tovariable informa- objects become classify (novae, supernova necessary. counterparts candidates Such of by GW knownenly types, alerts, classified but kilonovae, as GRB to SN afterglows) reveal and that other whatphysical were is properties mistak- even — more anomalies. important to Findingof detect high such astronomical priority objects objects and (and one with then of strange studying the main them aims more of closely) the is current study. processes. The to introduce the correlation betweenwhich peculiar the Type filters. 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