https://doi.org/10.1140/epjp/s13360-025-06419-5
Regular Article
Novel design of deep learning knowledge-driven recurrent neurostructure for bioconvective Maxwell nanofluid flow model with convective boundary and variable thermal conductivity
1
Department of Data Science and AI Applications, Graduate School of Engineering Science and Technology, National Yunlin University of Science and Technology, 64002, Yunlin, Taiwan
2
Department of Computer Science and Information Engineering, National Yunlin University of Science and Technology, 64002, Yunlin, Taiwan
3
Department of Computer Science and Information Engineering, Graduate School of Engineering Science and Technology, National Yunlin University of Science and Technology, 64002, Yunlin, Taiwan
4
International Graduate School of Artificial Intelligence, National Yunlin University of Science and Technology, 123 University Road, Section 3, 64002, Douliou, Yunlin, Taiwan, R.O.C.
5
AI Center, Yuan Ze University, 320, Taoyuan, Taiwan
6
Department of Safety, Health and Environmental Engineering, National Yunlin University of Science and Technology, 123 University Road, Section 3, 64002, Douliou, Yunlin, Taiwan, ROC
Received:
16
April
2025
Accepted:
12
May
2025
Published online:
2
June
2025
The significance of computational fluid dynamics (CFD) has paramount interest to simulate the dynamics of fluid flows, heat transfer, and relative processes extensively applicable in aerospace, energy, automation, and biomedical engineering industries for optimize designs, modeling and productivity. Artificial intelligence knowledge-driven machine learning-approaches can effectively reduce simulation time, improve precision, and make top-notch outcome of CFD simulations. The presented study stochastic numerical paradigm is exploited to determine the bioconvective flow of Maxwell nanofluidic (BCFM-NF) model with impact of thermal conductivity and convective boundary conditions using deep recurrent neural network trained with the Levenberg–Marquardt backpropagation (RNN-LMB). The BCFM-NF model is governed by partial differential equations (PDEs) that are further transformed into nonlinear ordinary differential equations (ODEs) by using similarity transformations. Synthetic dataset acquired for the BCFM-NF model with Adams numerical method by varying Maxwell parameter, and numbers, i.e., Lewis, Hartmann and Prandtl, while fixed values of mean absorption coefficient, Brownian diffusion, variable thermal conductivity etc. The generated dataset is used for execution of RNN-LMB algorithm to optimize the mean square error (MSE)-based objective function in order to get the approximated solutions for each case of all scenarios of BCFM-NF system with negligible error magnitude. The efficacy of RNN-LMB is certified accordingly by the convergence curves on iterative update of MSE, training state dynamics of adaptive controlling indices, frequency pattern in the error histograms, and correlation of error, autocorrelation statistics on exhaustive numerical simulations for BCFM-NF model.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
