Deep-learning based reconstruction of the shower maximum Xmax using the water-Cherenkov detectors of the Pierre Auger Observatory Aab, A. Carceller López, Juan Miguel Bueno Villar, Antonio Pierre Auger Collaboration Data analysis Pattern recognition, cluster finding, calibration and fitting methods Large detector systems for particle and astroparticle physics Particle identification methods The successful installation, commissioning, and operation of the Pierre Auger Observatory would not have been possible without the strong commitment and effort from the technical and administrative staff in Malargue. We are very grateful to the following agencies and organizations for financial support. Argentina - Comision Nacional de Energia Atomica; Agencia Nacional de Promocion Cientifica y Tecnologica (ANPCyT); Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET); Gobierno de la Provincia de Mendoza; Municipalidad de Malargue; NDM Holdings and Valle Las Lenas; in gratitude for their continuing cooperation over land access; Australia -the Australian Research Council; Brazil - Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPq); Financiadora de Estudos e Projetos (FINEP); Fundacao de Amparo a Pesquisa do Estado de Rio de Janeiro (FAPERJ); Sao Paulo Research Foundation (FAPESP) Grants No. 2019/10151-2, No. 2010/07359-6 and No. 1999/05404-3; Ministerio da Ciencia, Tecnologia, Inovacoes e Comunicacoes (MCTIC); Czech Republic Grant No. MSMT CR LTT18004, LM2015038, LM2018102, CZ.02.1.01/0.0/0.0/16_013/0001402, CZ.02.1.01/0.0/0.0/18_046/0016010 and CZ.02.1.01/0.0/0.0/17_049/0008422; France -Centre de Calcul IN2P3/CNRS; Centre National de la Recherche Scientifique (CNRS); Conseil Regional Ile-de-France; Departement Physique Nucleaire et Corpusculaire (PNC-IN2P3/CNRS); Departement Sciences de l'Univers (SDU-INSU/CNRS); Institut Lagrange de Paris (ILP) Grant No. LABEX ANR-10-LABX-63 within the Investissements d'Avenir Programme Grant No. ANR-11-IDEX-0004-02; Germany-Bundesministerium fur Bildung und Forschung (BMBF); Deutsche Forschungsgemeinschaft (DFG); Finanzministerium Baden-Wurttemberg; Helmholtz Alliance for Astroparticle Physics (HAP); Helmholtz-Gemeinschaft Deutscher Forschungszentren (HGF); Ministerium fur Innovation, Wissenschaft und Forschung des Landes Nordrhein-Westfalen; Ministerium fur Wissenschaft, Forschung und Kunst des Landes Baden-Wurttemberg; Italy - Istituto Nazionale di Fisica Nucleare (INFN); Istituto Nazionale di Astrofisica (INAF); Ministero dell'Istruzione, dell'Universita e della Ricerca (MIUR); CETEMPS Center of Excellence; Ministero degli Affari Esteri (MAE); Mexico-Consejo Nacional de Ciencia y Tecnologia (CONACYT) No. 167733; Universidad Nacional Autonoma de Mexico (UNAM); PAPIIT DGAPA-UNAM; The Netherlands - Ministry of Education, Culture and Science; Netherlands Organisation for Scientific Research (NWO); Dutch national e-infrastructure with the support of SURF Cooperative; Poland - Ministry of Science and Higher Education, grant No. DIR/WK/2018/11; National Science Centre, Grants No. 2013/08/M/ST9/00322, No. 2016/23/B/ST9/01635 and No. HARMONIA 5-2013/10/M/ST9/00062, UMO-2016/22/M/ST9/00198; Portugal - Portuguese national funds and FEDER funds within Programa Operacional Factores de Competitividade through Fundacao para a Ciencia e a Tecnologia (COMPETE); Romania-Romanian Ministry of Education and Research, the Program Nucleu within MCI (PN19150201/16N/2019 and PN-19060102) and project PNIII-P1-1.2-PCCDI-2017-0839/19PCCDI/2018 within PNCDI III; Slovenia - Slovenian Research Agency, grants P1-0031, P1-0385, I0-0033, N1-0111; Spain - Ministerio de Economia, Industria y Competitividad (FPA2017-85114-P and PID2019-104676GB-C32, Xunta de Galicia (ED431C 2017/07), Junta de Andalucia (SOMM17/6104/UGR, P18-FR-4314) Feder Funds, RENATA Red Nacional Tematica de Astroparticulas (FPA2015-68783-REDT) and Maria de Maeztu Unit of Excellence (MDM-2016-0692); USA -Department of Energy, Contracts No. DE-AC02-07CH11359, No. DE-FR02-04ER41300, No. DE-FG02-99ER41107 and No. DE-SC0011689; National Science Foundation, Grant No. 0450696; The Grainger Foundation; Marie Curie-IRSES/EPLANET; European Particle Physics Latin American Network; and UNESCO. The atmospheric depth of the air shower maximum X-max is an observable commonly used for the determination of the nuclear mass composition of ultra-high energy cosmic rays. Direct measurements of X-max are performed using observations of the longitudinal shower development with fluorescence telescopes. At the same time, several methods have been proposed for an indirect estimation of X-max from the characteristics of the shower particles registered with surface detector arrays. In this paper, we present a deep neural network (DNN) for the estimation of X-max The reconstruction relies on the signals induced by shower particles in the ground based water-Cherenkov detectors of the Pierre Auger Observatory. The network architecture features recurrent long short-term memory layers to process the temporal structure of signals and hexagonal convolutions to exploit the symmetry of the surface detector array. We evaluate the performance of the network using air showers simulated with three different hadronic interaction models. Thereafter, we account for long-term detector effects and calibrate the reconstructed X-max using fluorescence measurements. Finally, we show that the event-by-event resolution in the reconstruction of the shower maximum improves with increasing shower energy and reaches less than 25 g/cm(2) at energies above 2x10(19) eV. United States Department of Energy (DOE) DE-AC02-07CH11359 - DE-FR02-04ER41300 - DE- FG02-99ER41107 - DE-SC0011689 2021-11-09T11:08:37Z 2021-11-09T11:08:37Z 2021-07-14 info:eu-repo/semantics/article The Pierre Auger collaboration et al 2021 JINST 16 P07019. [https://doi.org/10.1088/1748-0221/16/07/P0701] http://hdl.handle.net/10481/71386 10.1088/1748-0221/16/07/P0701 eng http://creativecommons.org/licenses/by/3.0/es/ info:eu-repo/semantics/openAccess Atribución 3.0 España IOP