{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:06:21Z","timestamp":1760148381480,"version":"build-2065373602"},"reference-count":25,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2023,4,28]],"date-time":"2023-04-28T00:00:00Z","timestamp":1682640000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003141","name":"CONACYT M\u00e9xico","doi-asserted-by":"publisher","award":["CB258068"],"award-info":[{"award-number":["CB258068"]}],"id":[{"id":"10.13039\/501100003141","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>It is well-known that part of the neural networks capacity is determined by their topology and the employed training process. How a neural network should be designed and how it should be updated every time that new data is acquired, is an issue that remains open since it its usually limited to a process of trial and error, based mainly on the experience of the designer. To address this issue, an algorithm that provides plasticity to recurrent neural networks (RNN) applied to time series forecasting is proposed. A decision-making grow and prune paradigm is created, based on the calculation of the data\u2019s order, indicating in which situations during the re-training process (when new data is received), should the network increase or decrease its connections, giving as a result a dynamic architecture that can facilitate the design and implementation of the network, as well as improve its behavior. The proposed algorithm was tested with some time series of the M4 forecasting competition, using Long-Short Term Memory (LSTM) models. Better results were obtained for most of the tests, with new models both larger and smaller than their static versions, showing an average improvement of up to 18%.<\/jats:p>","DOI":"10.3390\/a16050231","type":"journal-article","created":{"date-parts":[[2023,4,28]],"date-time":"2023-04-28T04:36:15Z","timestamp":1682656575000},"page":"231","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Order-Based Schedule of Dynamic Topology for Recurrent Neural Network"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0009-0007-3806-7445","authenticated-orcid":false,"given":"Diego","family":"Sanchez Narvaez","sequence":"first","affiliation":[{"name":"Department of Computer Science, University of Guadalajara, 1421 Marcelino Garcia Barragan, Guadalajara 44430, Jalisco, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0802-0121","authenticated-orcid":false,"given":"Carlos","family":"Villase\u00f1or","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Guadalajara, 1421 Marcelino Garcia Barragan, Guadalajara 44430, Jalisco, Mexico"}]},{"given":"Carlos","family":"Lopez-Franco","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Guadalajara, 1421 Marcelino Garcia Barragan, Guadalajara 44430, Jalisco, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8803-9502","authenticated-orcid":false,"given":"Nancy","family":"Arana-Daniel","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Guadalajara, 1421 Marcelino Garcia Barragan, Guadalajara 44430, Jalisco, Mexico"}]}],"member":"1968","published-online":{"date-parts":[[2023,4,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1016\/j.ijforecast.2019.03.017","article-title":"A hybrid method of exponential smoothing and recurrent","volume":"36","author":"Slawek","year":"2020","journal-title":"Int. J. Forecast."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1016\/j.eswa.2022.119140","article-title":"What is the best RNN-cell structure to forecast each time series behavior?","volume":"215","author":"Khaldi","year":"2023","journal-title":"Expert Syst. Appl."},{"unstructured":"Peixeiro, M. (2022). Time Series Forecasting in Python, Manning. [1st ed.].","key":"ref_3"},{"unstructured":"Haykin, S. (2009). Neural Networks and Learning Machines, Pearson. [3rd ed.].","key":"ref_4"},{"key":"ref_5","first-page":"831","article-title":"Principles of Risk Minimization for Learning Theory","volume":"4","author":"Vapnik","year":"1992","journal-title":"Adv. Neural Inf. Process."},{"key":"ref_6","first-page":"215","article-title":"An Incremental Learning Algorithm That Optimizes Network Size and Sample Size in One Trial","volume":"1","year":"1991","journal-title":"IEEE Int. Conf. Neural Netw."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1162\/neco.1989.1.1.151","article-title":"What Size Net Gives Valid Generalization?","volume":"1","author":"Baum","year":"1989","journal-title":"Neural Comput."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1243","DOI":"10.1016\/j.ifacol.2020.12.1342","article-title":"On the vanishing and exploding gradient problem in Gated Recurrent Units","volume":"53","author":"Rehmer","year":"2020","journal-title":"IFAC-PapersOnLine"},{"unstructured":"Tsay, R.S., and Chen, R. (2019). Nonlinear Time Series Analysis, Wiley. [1st ed.].","key":"ref_9"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1109\/TC.2019.2954495","article-title":"Grow and Prune Compact, Fast and Accurate LSTMs","volume":"69","author":"Dai","year":"2020","journal-title":"IEEE Trans. Comput."},{"unstructured":"Blalock, D., Gonzalez Ortiz, J.J., Frankle, J., and Guttag, J. (2020, January 2\u20134). What is the State of Neural Network Pruning?. Proceedings of the 3rd MLSys Conference, Austin, TX, USA.","key":"ref_11"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1441","DOI":"10.1016\/0893-6080(94)90091-4","article-title":"Growing cell structures\u2014A self-organizing network for unsupervised and supervised learning","volume":"7","author":"Fritzke","year":"1994","journal-title":"Neural Netw."},{"key":"ref_13","first-page":"599","article-title":"Plasticidad cerebral, una realidad neuronal","volume":"23","author":"Benitez","year":"2019","journal-title":"Rev. De Cienc. M\u00e9dicas De Pinar Del R\u00edo"},{"key":"ref_14","first-page":"43","article-title":"Practical method for determining the minimum embedding dimension of a scalar time series","volume":"110","author":"Cao","year":"1997","journal-title":"Elsevier Sci."},{"key":"ref_15","first-page":"3403","article-title":"Determining embedding dimension for phase-space reconstruction using a geometrical construction","volume":"45","author":"Kennel","year":"1992","journal-title":"Am. Phys. Soc."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1016\/j.ijforecast.2019.04.014","article-title":"The M4 Competition: 100,000 time series and 61 forecasting methods","volume":"36","author":"Makridakis","year":"2020","journal-title":"Int. J. Forecast."},{"unstructured":"Sanchez, E.N., and Felix, R.A. (2002, January 21\u201326). Nonlinear identification via variable structure recurrent neural networks. Proceedings of the 15th Triennial World Congress, Barcelona, Spain.","key":"ref_17"},{"key":"ref_18","first-page":"146","article-title":"Generaci\u00f3n din\u00e1mica de la topolog\u00eda de una red neuronal artificial del tipo perceptron multicapa, Revista Facultad de Ingenieria","volume":"38","author":"Tabares","year":"2006","journal-title":"Univ. De Antioq."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"8675","DOI":"10.1007\/s00521-019-04359-7","article-title":"A dynamic ensemble learning algorithm for neural networks","volume":"32","author":"Alam","year":"2019","journal-title":"Neural Comput. Appl."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"752","DOI":"10.1109\/TETC.2020.3037052","article-title":"Incremental Learning Using a Grow and Prune Paradigm with Efficient Neural Networks","volume":"10","author":"Dai","year":"2020","journal-title":"IEEE Trans. Emerg. Top. Comput."},{"unstructured":"Chollet, F. (2018). Deep Learning with Python, Manning Publications Co.","key":"ref_21"},{"unstructured":"Olah, C. (2022, October 20). Github-Understanding LSTM Networks. Available online: https:\/\/colah.github.io\/posts\/2015-08-Understanding-LSTMs\/.","key":"ref_22"},{"key":"ref_23","first-page":"2148","article-title":"Predicting Parameters in Deep Learning","volume":"2","author":"Denil","year":"2013","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1016\/j.ijforecast.2018.12.007","article-title":"Are forecasting competitions data representative of the reality?","volume":"1","author":"Spiliotis","year":"2020","journal-title":"Int. J. Forecast."},{"unstructured":"Yogesh, S. (2022, October 21). Kaggle-M4 Forecasting Competition Dataset. Available online: https:\/\/www.kaggle.com\/datasets\/yogesh94\/m4-forecasting-competition-dataset.","key":"ref_25"}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/16\/5\/231\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:25:28Z","timestamp":1760124328000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/16\/5\/231"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,4,28]]},"references-count":25,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2023,5]]}},"alternative-id":["a16050231"],"URL":"https:\/\/doi.org\/10.3390\/a16050231","relation":{},"ISSN":["1999-4893"],"issn-type":[{"type":"electronic","value":"1999-4893"}],"subject":[],"published":{"date-parts":[[2023,4,28]]}}}