{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:43:57Z","timestamp":1760060637118,"version":"build-2065373602"},"reference-count":45,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,9,13]],"date-time":"2025-09-13T00:00:00Z","timestamp":1757721600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Open Access Publication Fund of South Westphalia University of Applied Sciences"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["MAKE"],"abstract":"<jats:p>Interpretable decision-making algorithms are important when used in the context of production optimization. While concepts like Petri nets are inherently interpretable, they are not straightforwardly learnable. This paper presents a novel approach to transform the Petri net model into a learnable entity. This is accomplished by establishing a relationship between the Petri net description in the event domain, its representation in the max-plus algebra, and a one-layer perceptron neural network. This allows us to apply standard supervised learning methods adapted to the max-plus domain to infer the parameters of the Petri net. To this end, the feed-forward and back-propagation paths are modified to accommodate the differing mathematical operations in the context of max-plus algebra. We apply our approach to a multi-robot handling system with potentially varying processing and operation times. The results show that essential timing parameters can be inferred from data with high precision.<\/jats:p>","DOI":"10.3390\/make7030100","type":"journal-article","created":{"date-parts":[[2025,9,15]],"date-time":"2025-09-15T07:56:51Z","timestamp":1757923011000},"page":"100","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Learnable Petri Net Neural Network Using Max-Plus Algebra"],"prefix":"10.3390","volume":"7","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1792-7748","authenticated-orcid":false,"given":"Mohammed Sharafath","family":"Abdul Hameed","sequence":"first","affiliation":[{"name":"Department of Automation Technology and Learning Systems, South Westphalia University of Applied Sciences, 59494 Soest, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7919-6939","authenticated-orcid":false,"given":"Sofiene","family":"Lassoued","sequence":"additional","affiliation":[{"name":"Department of Automation Technology and Learning Systems, South Westphalia University of Applied Sciences, 59494 Soest, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8405-0977","authenticated-orcid":false,"given":"Andreas","family":"Schwung","sequence":"additional","affiliation":[{"name":"Department of Automation Technology and Learning Systems, South Westphalia University of Applied Sciences, 59494 Soest, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,9,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"690","DOI":"10.1016\/j.jmsy.2024.04.028","article-title":"Introducing PetriRL: An innovative framework for JSSP resolution integrating Petri nets and event-based reinforcement learning","volume":"74","author":"Lassoued","year":"2024","journal-title":"J. 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