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We developed a new vectorized algorithm that takes the number of unknowns (state variables) and number of parameters into consideration. The algorithm, first, trains the network to determine weights and biases. Next, the algorithm solves the systems of algebraic equations to estimate the parameters of the system. If the right hand side function of the system is smooth and the system have equal numbers of unknowns and parameters, the algorithm solves the algebraic equation at the discrete point where absolute error between the neural network solutions and the measured data is minimum. This improves the accuracy and reduces computational time. Several tests were carried out in linear and non-linear dynamical systems. Last, we showed that the DNN approach is more successful in terms of computational time as the number of hidden layers increases.<\/jats:p>","DOI":"10.1155\/2022\/2014510","type":"journal-article","created":{"date-parts":[[2022,4,27]],"date-time":"2022-04-27T22:05:09Z","timestamp":1651097109000},"page":"1-10","source":"Crossref","is-referenced-by-count":3,"title":["Parameter Estimation for Dynamical Systems Using a Deep Neural Network"],"prefix":"10.1155","volume":"2022","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8612-7170","authenticated-orcid":true,"given":"Tamirat Temesgen","family":"Dufera","sequence":"first","affiliation":[{"name":"Applied Mathematics, Adama Science and Technology University, Adama 1888, Oromia, Ethiopia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5024-8950","authenticated-orcid":true,"given":"Yadeta Chimdessa","family":"Seboka","sequence":"additional","affiliation":[{"name":"Applied Mathematics, Adama Science and Technology University, Adama 1888, Oromia, Ethiopia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4322-0113","authenticated-orcid":true,"given":"Carlos","family":"Fresneda Portillo","sequence":"additional","affiliation":[{"name":"Departamento de M\u00e9todos Cuantitativos, Universidad Loyola Andaluc\u00eda, Avenida de Las Universidades, Dos Hermanas 41704, Sevilla, Spain"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1742-4658.2008.06844.x"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1016\/j.mib.2018.07.004"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2019.05.037"},{"key":"4","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4939-9828-9","volume-title":"Mathematical Models in Epidemiology","author":"F. 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