{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,22]],"date-time":"2026-03-22T14:57:53Z","timestamp":1774191473837,"version":"3.50.1"},"reference-count":96,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2020,1,30]],"date-time":"2020-01-30T00:00:00Z","timestamp":1580342400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000780","name":"European Commission","doi-asserted-by":"publisher","award":["ID 793505"],"award-info":[{"award-number":["ID 793505"]}],"id":[{"id":"10.13039\/501100000780","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003542","name":"Ministerium f\u00fcr Wissenschaft, Forschung und Kunst Baden-W\u00fcrttemberg","doi-asserted-by":"publisher","award":["NaMoCa"],"award-info":[{"award-number":["NaMoCa"]}],"id":[{"id":"10.13039\/501100003542","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004543","name":"China Scholarship Council","doi-asserted-by":"publisher","award":["20120673003"],"award-info":[{"award-number":["20120673003"]}],"id":[{"id":"10.13039\/501100004543","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades. Gobierno de Espa\u00f1a. &quot;Programa Estatal de I+D+i Orientada a los Retos de la Sociedad&quot;. Big analytics tHrough IIoT and blockchaIN technoloGies for Smart MAintenance Strategies","award":["RTI2018-094614-B-I00: Smashing"],"award-info":[{"award-number":["RTI2018-094614-B-I00: Smashing"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In the near future, value streams associated with Industry 4.0 will be formed by interconnected cyber\u2013physical elements forming complex networks that generate huge amounts of data in real time. The success or failure of industry leaders interested in the continuous improvement of lean management systems in this context is determined by their ability to recognize behavioral patterns in these big data structured within non-Euclidean domains, such as these dynamic sociotechnical complex networks. We assume that artificial intelligence in general and deep learning in particular may be able to help find useful patterns of behavior in 4.0 industrial environments in the lean management of cyber\u2013physical systems. However, although these technologies have meant a paradigm shift in the resolution of complex problems in the past, the traditional methods of deep learning, focused on image or video analysis, both with regular structures, are not able to help in this specific field. This is why this work focuses on proposing geometric deep lean learning, a mathematical methodology that describes deep-lean-learning operations such as convolution and pooling on cyber\u2013physical Industry 4.0 graphs. Geometric deep lean learning is expected to positively support sustainable organizational growth because customers and suppliers ought to be able to reach new levels of transparency and traceability on the quality and efficiency of processes that generate new business for both, hence generating new products, services, and cooperation opportunities in a cyber\u2013physical environment.<\/jats:p>","DOI":"10.3390\/s20030763","type":"journal-article","created":{"date-parts":[[2020,2,5]],"date-time":"2020-02-05T03:18:48Z","timestamp":1580872728000},"page":"763","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":27,"title":["Geometric Deep Lean Learning: Deep Learning in Industry 4.0 Cyber\u2013Physical Complex Networks"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2423-1474","authenticated-orcid":false,"given":"Javier","family":"Villalba-D\u00edez","sequence":"first","affiliation":[{"name":"Fakultaet fuer Management und Vertrieb, Campus Schw\u00e4bisch-Hall, Hochschule Heilbronn, 74523 Schw\u00e4bisch-Hall, Germany"},{"name":"Department of Artificial Intelligence, Universidad Polit\u00e9cnica de Madrid, Campus de Montegancedo, 28660 Boadilla del Monte, Madrid, Spain"},{"name":"Escuela T\u00e9cnica Superior de Ingenieros Industriales, Universidad Polit\u00e9cnica de Madrid, Jos\u00e9 Guti\u00e9rrez Abascal 2, 28006 Madrid, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7145-1974","authenticated-orcid":false,"given":"Martin","family":"Molina","sequence":"additional","affiliation":[{"name":"Department of Artificial Intelligence, Universidad Polit\u00e9cnica de Madrid, Campus de Montegancedo, 28660 Boadilla del Monte, Madrid, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9677-6764","authenticated-orcid":false,"given":"Joaqu\u00edn","family":"Ordieres-Mer\u00e9","sequence":"additional","affiliation":[{"name":"Escuela T\u00e9cnica Superior de Ingenieros Industriales, Universidad Polit\u00e9cnica de Madrid, Jos\u00e9 Guti\u00e9rrez Abascal 2, 28006 Madrid, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8790-7371","authenticated-orcid":false,"given":"Shengjing","family":"Sun","sequence":"additional","affiliation":[{"name":"Escuela T\u00e9cnica Superior de Ingenieros Industriales, Universidad Polit\u00e9cnica de Madrid, Jos\u00e9 Guti\u00e9rrez Abascal 2, 28006 Madrid, Spain"},{"name":"Exposure, Epidemiology, and Risk Program, Department of Environmental Health, Harvard T.H. Chan School of Public Health, Boston, MA 02115, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8917-2041","authenticated-orcid":false,"given":"Daniel","family":"Schmidt","sequence":"additional","affiliation":[{"name":"Escuela T\u00e9cnica Superior de Ingenieros Industriales, Universidad Polit\u00e9cnica de Madrid, Jos\u00e9 Guti\u00e9rrez Abascal 2, 28006 Madrid, Spain"},{"name":"Lead Developer Quality Inspection, Matthews International GmbH, Gutenbergstra\u00dfe 1-3, 48691 Vreden, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4882-029X","authenticated-orcid":false,"given":"Wanja","family":"Wellbrock","sequence":"additional","affiliation":[{"name":"Fakultaet fuer Management und Vertrieb, Campus Schw\u00e4bisch-Hall, Hochschule Heilbronn, 74523 Schw\u00e4bisch-Hall, Germany"}]}],"member":"1968","published-online":{"date-parts":[[2020,1,30]]},"reference":[{"key":"ref_1","unstructured":"Reinsel, D., Gantz, J., and Rydning, J. (2020, January 30). The Digitization of the World. 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