{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:23:36Z","timestamp":1760243016668,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2015,4,1]],"date-time":"2015-04-01T00:00:00Z","timestamp":1427846400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this work, we begin by considering the qualitative modeling of biological regulatory systems using process hitting, from which we define its probabilistic counterpart by considering the chemical master equation within a kinetic theory framework. The last equation is efficiently solved by considering a separated representation within the proper generalized decomposition framework that allows circumventing the so-called curse of dimensionality. Finally, model parameters can be added as extra-coordinates in order to obtain a parametric solution of the model.<\/jats:p>","DOI":"10.3390\/e17041896","type":"journal-article","created":{"date-parts":[[2015,4,7]],"date-time":"2015-04-07T03:47:46Z","timestamp":1428378466000},"page":"1896-1915","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Kinetic Theory Modeling and Efficient Numerical Simulation of Gene Regulatory Networks Based on Qualitative Descriptions"],"prefix":"10.3390","volume":"17","author":[{"given":"Francisco","family":"Chinesta","sequence":"first","affiliation":[{"name":"GeM , Ecole Centrale de Nantes, 1 rue de la Noe, 44300 Nantes, France"}]},{"given":"Morgan","family":"Magnin","sequence":"additional","affiliation":[{"name":"IRCCyN, Ecole Centrale de Nantes, 1 rue de la Noe, 44300 Nantes, France"}]},{"given":"Olivier","family":"Roux","sequence":"additional","affiliation":[{"name":"IRCCyN, Ecole Centrale de Nantes, 1 rue de la Noe, 44300 Nantes, France"}]},{"given":"Amine","family":"Ammar","sequence":"additional","affiliation":[{"name":"LAMPA, ENSAM Angers, 2 Boulevard du Ronceray, BP 93525, 49035 Angers Cedex 01, France"}]},{"given":"Elias","family":"Cueto","sequence":"additional","affiliation":[{"name":"Universidad de Zaragoza. 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