Kumar, Harender and Yadav, Neha and Nagar, Atulya K. (2022) Numerical solution of Generalized Burger-Huxley & Huxley’s equation using Deep Galerkin neural network method. Engineering Applications of Artificial Intelligence, 115. ISSN 0952-1976
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Abstract
In this paper, a deep learning algorithm based on Deep Galerkin method (DGM) is presented for the approximate solution of the generalized Burgers-Huxley equation (gBHE), and generalized Hux-ley’s equation (gHE). In this method, a deep neural network (DNN) is used for approximating the solution without generating mesh grid, which satisfies the di˙erential operator, boundary and initial conditions. DNN is trained on randomly selected batches of time and space points, thus helping to avoid forming a mesh. Adam optimizer is used for optimizing the parameters of the DNN. Further, the convergence of the cost function and convergence of the neural network to the exact solution is demonstrated. This method shows very encouraging results which have been compared with re-cent methods such as: A fourth order improved numerical scheme(FDS4), Adomain-decomposition method (ADM), Modified cubic B-spline di˙erential quadrature method (MCB- DQM), Variational iteration method(VIM), and others.
| Item Type: | Article |
|---|---|
| Additional Information and Comments: | “NOTICE: this is the author’s version of a work that was accepted for publication in Engineering Applications of Artificial Intelligence. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Engineering Applications of Artificial Intelligence, Volume 115, October 2022, https://doi.org/10.1016/j.engappai.2022.105289 |
| Keywords: | Deep learning, Deep neural network, GRU network, Adam optimizer, Generalized Burger-Huxley & Huxley’s equation |
| Faculty / Department: | Faculty of Human and Digital Sciences > Mathematics and Computer Science |
| Depositing User: | Atulya Nagar |
| Date Deposited: | 06 Sep 2022 14:47 |
| Last Modified: | 15 Aug 2024 00:15 |
| URI: | https://hira.hope.ac.uk/id/eprint/3593 |
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