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In this paper, we investigate mathematical models of biofiltration for mixing volatile organic compounds (VOCs) for instance hydrophilic (methanol) and hydrophobic (\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$\\alpha$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mi>\u03b1<\/mml:mi>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    -pinene). The system of nonlinear diffusion equations describes the Michaelis-Menten kinetics of the enzymic chemical reaction. These models represent the chemical oxidation in the gas phase and mass transmission within the air-biofilm junction. Furthermore, for the numerical study of the saturation of\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$\\alpha$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mi>\u03b1<\/mml:mi>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    -pinene and methanol in the biofilm and gas state, we have developed an efficient supervised machine learning algorithm based on the architecture of Elman neural networks (ENN). Moreover, the Levenberg-Marquardt (LM) optimization paradigm is used to find the parameters\/ neurons involved in the ENN architecture. The approximation to a solutions found by the ENN-LM technique for methanol saturation and\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$\\alpha$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mi>\u03b1<\/mml:mi>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    -pinene under variations in different physical parameters are allegorized with the numerical results computed by state-of-the-art techniques. The graphical and statistical illustration of indications of performance relative to the terms of absolute errors, mean absolute deviations, computational complexity, and mean square error validates that our results perfectly describe the real-life situation and can further be used for problems arising in chemical engineering.\n                  <\/jats:p>","DOI":"10.1038\/s41598-024-65153-7","type":"journal-article","created":{"date-parts":[[2024,7,23]],"date-time":"2024-07-23T12:10:43Z","timestamp":1721736643000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Mathematical modeling and machine learning-based optimization for enhancing biofiltration efficiency of volatile organic compounds"],"prefix":"10.1038","volume":"14","author":[{"given":"Muhammad","family":"Sulaiman","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Osamah Ibrahim","family":"Khalaf","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Naveed Ahmad","family":"Khan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fahad Sameer","family":"Alshammari","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Habib","family":"Hamam","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2024,7,23]]},"reference":[{"key":"65153_CR1","doi-asserted-by":"publisher","first-page":"237","DOI":"10.1016\/S1369-5266(02)00251-0","volume":"5","author":"E Pichersky","year":"2002","unstructured":"Pichersky, E. & Gershenzon, J. 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